{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# CS 237 Spring 2021, HW 11 \n", "\n", "#### Due date: Friday April 23rd at Midnight (1 minute after 11:59pm on 4/23) via Gradescope (with a 6 hour grace period)\n", "\n", " Late policy: You may submit the homework up to 24 hours late for a 10% penalty. Hence, the late deadline is Saturday 4/24 at Midnight (with a 6 hour grace period). \n", "\n", "#### General Instructions\n", "\n", "Please complete this notebook by filling in solutions where indicated. \n", "\n", "For full credit, please take careful note of the following requirements:\n", "\n", "- Do NOT use any HTML tags in your notebook, as Gradescope will ignore them;\n", "\n", "- Do NOT answer questions by including images, as Gradescope will ignore them; and \n", "\n", "- You MUST \"Restart and Run All\" from the Kernel menu before submitting to Gradescope.\n", "\n", "- You must present all numbers in readable form (approximately 4 digits of precision) unless otherwise stated. \n", "\n", "**Any assignments which do not follow these requirements will not receive full credit.** \n", "\n", "\n", "\n", "There are 8 problems on this homework, 4 on confidence intervals and 4 on hypothesis testing. In each group of 4, the first three will involve \"made-up\" data and the 4th will involve using Pandas to calculate with real data. " ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "# Here are some imports which will be used in code that we write for CS 237\n", "\n", "import matplotlib.pyplot as plt # normal plotting\n", "import numpy as np\n", "import pandas as pd\n", "\n", "from math import log, pi, log, floor, ceil # import whatever you want from math\n", "#from random import seed, random\n", "from collections import Counter\n", "\n", "\n", "%matplotlib inline\n", "\n", "from scipy.special import comb\n", " \n", "def C(N,K): \n", " return comb(N,K,True) # just a wrapper around the scipy function\n", "\n", "\n", "def round4(x):\n", " return np.around(x,4)\n", "\n", "\n", "# Here are the basic statistical functions we will use from numpy\n", "\n", "from numpy import mean, var, std, median, sqrt\n", "\n", "from numpy.random import choice, seed\n", "\n", "L = [2,4,3,6,4,5]\n", "\n", "# mean value\n", "\n", "mean(L) \n", "\n", "\n", "# Variance\n", "# ddof = delta degrees of freedom, default is 0\n", "\n", "# population variance\n", "var(L) \n", "\n", "# sample variance\n", "var(L,ddof=1)\n", "\n", "# Standard deviation\n", "# ddof = delta degrees of freedom, reduction in degrees of freedom:\n", "# for population stdev, this is 0 (the default value)\n", "# for sample stdev, should be 1\n", "\n", "# population standard deviation\n", "std(L) \n", "\n", "# sample standard deviation\n", "std(L,ddof=1) \n", "\n", "# Median\n", "\n", "median(L) \n", "\n", "# Random sampling of `size` elements from list with or without replacement\n", "\n", "np.random.choice(L,size=1,replace=True)\n", " \n", "# Scipy statistical functions\n", "\n", "from scipy.stats import norm, binom, expon, geom, poisson, gamma, nbinom, bernoulli \n", "\n", "# https://docs.scipy.org/doc/scipy/reference/stats.html\n", "\n", "#### Normal Distribution #####\n", "\n", "###### Note that in this library loc = mean and scale = standard deviation #####\n", "\n", "# Examples assume random variable X (e.g., housing prices) normally distributed with mu = 60, sigma = 10\n", "\n", "# Probability Density Function (really only useful for drawing the curve)\n", "# f(x) = P(X == x)\n", "\n", "norm.pdf(x=50,loc=60, scale= 10) \n", "\n", "# Cumulative Density Function\n", "# F(x) = P(X < x)\n", "\n", "# Example: Percentage of houses less than 50K. \n", "norm.cdf(x=50,loc=60,scale=10) \n", "\n", "# Example: Find P(60 x)\n", "\n", "# Example: Percentage of houses more than 50K.\n", "norm.sf(x=50,loc=60,scale=10) \n", "\n", "# Percentage Point Function: Inverse of the CDF:\n", "# For what is the largest value of k for which P( X < k ) = q ?\n", "\n", "# Example: What is the maximum cost of the 5% cheapest houses, \n", "# i.e., the x such that P(X < x) = 0.05?\n", "\n", "norm.ppf(q=0.05,loc=60,scale=40)\n", "\n", "# Inverse Survival Function: Inverse (1 - CDF):\n", "# For what is the smallest value of k for which P( X > k ) = q ?\n", "\n", "# Example: What is the minimum cost of the 5% most expensive houses, \n", "# i.e., the x such that P(X > x) = 0.05?\n", "\n", "norm.isf(q=0.05,loc=60,scale=40)\n", "\n", "# Give the endpoints of the interval (centered on the mean)\n", "# which contain alpha/100 percent of the population (alpha is a probability)\n", "\n", "# Ex. Give the interval for the middle 75% of the houses\n", "\n", "norm.interval(alpha=0.75, loc=60, scale=40)\n", "\n", "# generate a random variate\n", "norm.rvs(loc=60, scale=40)\n", "\n", "# generate random variates, returns list of length = size\n", "norm.rvs(loc=60, scale=40, size=10)\n", "\n", "\n", "\n", "\n", "##### Exponential Distribution ########\n", "\n", "##### loc = minimum value (leave at 0 always) ##### \n", "##### scale = mean = 1 / lambda (using textbook notation) #####\n", "\n", "# Probability Density Function f(x) (Only useful for graphing and showing shape)\n", "\n", "lam = 4\n", "expon.pdf(x=5,loc=0, scale=1/lam) # Must use 'scale = 1/lambda' to be consistent with textbook and lecture \n", "\n", "# Cumulative Density Function\n", "# F(x) = P(X < x)\n", "\n", "expon.cdf(x=5,loc=0,scale=1/lam) \n", "\n", "# Example: Find P(6 x)\n", "\n", "expon.sf(x=5,loc=0,scale=1/lam) \n", "\n", "# Inverse Survival Function: Inverse (1 - CDF):\n", "# For what is the value of k for which P( X > k ) = q ?\n", "\n", "expon.isf(q=0.05,loc=0,scale=1/lam)\n", "\n", "#g. generate a random variate\n", "expon.rvs(loc=0, scale=1/lam)\n", "\n", "#h. generate random variates, returns list of length = size\n", "expon.rvs(loc=0, scale=1/lam, size=10)\n", "\n", "# Same for Poisson, nbinom, gamma, bernoulli, etc. as shown here:\n", "\n", "##### Bernoulli Distribution X ~ Bernoulli(p) ####\n", "\n", "# p = probability of success for Bernoulli trial\n", "\n", "# Generate a random variate\n", "bernoulli.rvs(p=0.5)\n", "\n", "# Generate a list of random variates\n", "bernoulli.rvs(p=0.5,size=100)\n", "\n", "##### Binomial Distribution X ~ B(n,p) ####\n", "\n", "# n = number of independent Bernoulli trials\n", "# p = probability of success for Bernoulli trial\n", "# k = outcome in range [0 .. n]\n", "\n", "# Generate a random variate\n", "binom.rvs(n=10, p=0.5)\n", "\n", "# Generate a list of random variates\n", "binom.rvs(n=10, p=0.5,size=100)\n", "\n", "# Probability mass function: P(X = k)\n", "binom.pmf(k=4, n=10, p=0.5)\n", "\n", "# Cumulative distribution function: P(X <= k)\n", "binom.cdf(k=4, n=10, p=0.5)\n", "\n", "\n", "# percent error\n", "\n", "def PE(observed, expected):\n", " return (observed - expected) / expected\n", "\n", "print()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem One \n", "\n", "For this problem, we will write some functions which will be useful in the rest of\n", "the homework. Fill in the template below and verify correctness as shown. \n", "\n", "Hint: You may find the `norm.interval(...)` function useful. \n", "\n", "### Part A (Confidence Intervals)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n", "0\n", "0\n", "0\n" ] } ], "source": [ "# For confidence intervals: Convert from a confidence level to a k value\n", "# representing the number of standard deviations away from the mean (following the lecture slides)\n", "\n", "def CL2Std(CL):\n", " return 0 # just to get it to compile, put your code here\n", "\n", "\n", "def Std2CL(sigma):\n", " return 0 # just to get it to compile, put your code here\n", "\n", "\n", "# test them!\n", "\n", "# should print 1.95996398\n", "print(np.around(CL2Std(0.95),8))\n", "\n", "# should print 0.95449974\n", "print(np.around(Std2CL(2),8))\n", "\n", "# should return same value!\n", "print(np.around(Std2CL(CL2Std(0.1111)),4))\n", "\n", "# should return same value!\n", "print(np.around(CL2Std(Std2CL(0.9999)),4))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part B (Hypothesis Testing)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0 0]\n", "1.0\n", "0\n", "0.0062\n", "0\n", "0.5\n" ] } ], "source": [ "# For hypothesis testing: Convert from a level of significance to a pair of x values (for a two-sided test)\n", "# or a single x value (for one-sided tests)\n", "\n", "# For two-sided test, return numpy array [lb ub] for boundaries of the critical region of area equal to LOS\n", "# in N(mu,sigma^2)\n", "\n", "# mu is the hypothesis for the mean\n", "\n", "def LOS2Bounds(mu,sigma,LOS):\n", " return [0,0] # just to get it to compile, put your code here \n", "\n", "# For lower one-sided test, return lower bound for non-critical region (x value \n", "# at the boundary between the critical region below and the non-critical region above)\n", "# in N(mu,sigma^2)\n", "\n", "def LOS2LB(mu,sigma,LOS):\n", " return 0 # just to get it to compile, put your code here\n", "\n", "# For upper one-sided test, return upper bound for non-critical region (x value \n", "# at the boundary between the critical region above and the non-critical region below)\n", "# in N(mu,sigma^2)\n", "\n", "def LOS2UB(mu,sigma,LOS):\n", " return 0 # just to get it to compile, put your code here\n", "\n", "\n", "# Test them!\n", "\n", "# These examples are illustrated below in section on hypothesis testing\n", "\n", "# should print [21.0801 28.9199] \n", "bounds = LOS2Bounds(25,2,0.05)\n", "print(np.around(bounds,4))\n", "\n", "# should print LOS 0.05\n", "print(np.around(1-norm.cdf(bounds[1],25,2)+norm.cdf(bounds[0],25,2),4))\n", "\n", "# should return 2.4369 \n", "lb = LOS2LB(5,2,0.1)\n", "print(np.around(lb,4))\n", "\n", "# should print LOS 0.1\n", "print(np.around(norm.cdf(lb,5,2),4))\n", "\n", "# should return 1.6449 \n", "ub = LOS2UB(0,1,0.05)\n", "print(np.around(ub,4))\n", "\n", "# should print LOS 0.05\n", "print(np.around(1-norm.cdf(ub,0,1),4))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Two (Confidence Intervals) \n", "\n", "Suppose an experiment is conducted where 100 students at BU are measured and their average height is found to be 67.45 inches, and the (sample) standard deviation to be 2.93 inches. Since 100 is a large sample, we use\n", "the sample standard deviation as an estimate of the population standard deviation. We may assume that heights are normally distributed.\n", "\n", "(A) Suppose that you want to report the 95.45...% confidence interval (i.e., exactly 2 standard deviations). Give the results of this experiment as described in lecture. \n", "\n", "(B) Now suppose you want to report the precisely 95.0% confidence interval (which will be slightly less than 2 standard deviations -- find out the exact figure) Repeat (A) using this confidence interval. \n", "\n" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Solution (A)\n" ] } ], "source": [ "print(\"\\nSolution (A)\")\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Solution (B)\n" ] } ], "source": [ "print(\"\\nSolution (B)\")\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Three (Confidence Intervals)\n", "\n", "Suppose we want to estimate the lifetime of Apple iPads. An experiment is done where we sample 300 iPads to see how long they last, and the mean of this sample is found to be 3245.9 hours and the sample standard deviation to be 548.82 hours. \n", "\n", "(A) Report the mean lifetime of Apple iPads at a 95% level of confidence.\n", "\n", "(B) Report the same at a 99% level of confidence." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Solution (A):\n" ] } ], "source": [ "print(\"\\nSolution (A):\")\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Solution (B):\n" ] } ], "source": [ "print(\"\\nSolution (B):\")\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Four (Confidence Intervals on Real Data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part A\n", "\n", "First we will read in the biometric data on heights and weights from \n", "\n", "> https://cs-web.bu.edu/fac/snyder/cs237/Data/biometricdata.csv\n", "\n", "extract the weights into a Python list, find the ground truth about the mean and standard deviation,\n", "then perform a sampling experiment. \n", "\n", "In order to reinforce our understanding of the CLT, AND to test our sampling procedure, we will also\n", "verify that the predictions made by the CLT will be approximately correct. \n", "\n", "Complete the following template." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n" ] } ], "source": [ "# read biometric data into Pandas data frame:\n", "\n", "Bio = None # just to get it to compile, your code here\n", "\n", "# Convert column of all Weights into a Python list\n", "\n", "W = [ 0 ] # just to get it to compile, your code here\n", "\n", "\n", "\n", "population_mean = mean(W)\n", "population_std = std(W)\n", "\n", "\n", "print( ) # just to get it to compile, your code here\n", "\n", "# Randomly sample weight of N individuals return mean and *sample* standard deviation as a pair\n", "# Use choice from numpy.random\n", "# Ok to just do it with replace=True\n", "\n", "def get_sample_parameters(P,N):\n", " # just to get it to compile, your code here\n", " return (0,0) \n", "\n", "# test it!\n", "\n", "# Try it without the seed and watch what happens, then use the seed before submit\n", "\n", "seed(0)\n", "\n", "\n", "(x_bar_30,sigma_sample_30) = get_sample_parameters(W,30)\n", "\n", "\n", "print( ) # just to get it to compile, your code here \n", "\n", "seed(0)\n", "\n", "\n", "(x_bar_100,sigma_sample_100) = get_sample_parameters(W,100)\n" ] }, { "attachments": { "Screen%20Shot%202021-04-19%20at%203.31.00%20PM.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "Hint: You should get something very close to:\n", "\n", "![Screen%20Shot%202021-04-19%20at%203.31.00%20PM.png](attachment:Screen%20Shot%202021-04-19%20at%203.31.00%20PM.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part B\n", "\n", "Now we will warm up by verifying the CLT on our data: if we perform the sampling experiment for $N=100$ with\n", "$10^4$ trials, we should get a normal distribution with approximately the same mean. \n", "\n", "Complete the following template. " ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "# Collect together the sample means from 10**4 samples (you can ignore the sample standard deviations for now)\n", "\n", "# print out the mean of the collection of means, and also print out\n", "# the percent error compared with the ground truth value. Be sure to round to 4\n", "# decimal places and report the percent error as a percent (followed by \"%\"). \n", "\n", "num_trials = 10\n", "\n", "N = 100\n", "\n", "seed(0)\n", "\n", "sample_means = [ 0 ] # just to get it to compile, your code here\n", "\n", "mean_of_means = mean(sample_means)\n", "\n", "# print out mean_of_means and percent error compared with ground truth population_mean" ] }, { "attachments": { "Screen%20Shot%202021-04-19%20at%203.30.41%20PM.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "Hint: You should get something very close to:\n", "\n", "![Screen%20Shot%202021-04-19%20at%203.30.41%20PM.png](attachment:Screen%20Shot%202021-04-19%20at%203.30.41%20PM.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part C\n", "\n", "Now we do the same for the standard deviation, we should get an std which is reduced by a factor of 10. Use the same sample parameters as for Part B. " ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "# print out the standard deviation of the collection of means, and also print out\n", "# the percent error compared with the ground truth value. Be sure to round to 4\n", "# decimal places and report the percent error as a percent (followed by \"%\"). \n", "\n", "std_of_means = std(sample_means)\n", "\n" ] }, { "attachments": { "Screen%20Shot%202021-04-19%20at%203.30.48%20PM.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "Hint: You should get something very close to:\n", "\n", "![Screen%20Shot%202021-04-19%20at%203.30.48%20PM.png](attachment:Screen%20Shot%202021-04-19%20at%203.30.48%20PM.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part D\n", "\n", "Ok, finally let's do a sampling experiment and report our result using a confidence of 95 %. \n", "\n", "Complete the following template." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "#seed(0)\n", "\n", "# perform one sample and get parameters\n", "\n", "N = 100\n", "\n", "CL = 0.95\n", "\n", "seed(0)\n", "\n", "(x_bar,sigma_sample) = get_sample_parameters(W,N)\n", "\n", "\n", "# report the result with confidence interval, using CL = 0.95\n", "# Be sure to round to 4 decimal places and report the confidence level as a percent (followed by \"%\"). \n", "\n" ] }, { "attachments": { "Screen%20Shot%202020-03-28%20at%2012.35.26%20PM.png": { "image/png": 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OLd0+vU8GOENOI1ljfRN7Uw+zYPNoizjLRKsT1sk2KbZpdqfs0xySHGOcfJ3tXPT2aboa7Hc5EHUwx+0WqdW9y6PD875XofdhH0dfaT9KvwX/voCGwPKgguCMkIRQ8iFXslYYd9ha+FDEzcjkKPdo/RjpWP7DnEdYjzLG0RzDHFuOf3e8K+F2Yk5S1In9ySYn9VLMUklpx9OvnXp8euLM54ylsyuZS+e+Zy1mf8pZyP18/ucFmnyVguDC0os9l6Yuz1+Zufqm6GVxf8mTa02ljde7yj7d4K3YX1l482U1wy2L2ynw7rV6X7LGs7agbqAB/UC+8eDDE02lzY0tTY9utJ5tO9oe1RH/OKPz4pPip5e6zjyL6LZ9LtGD6hnrvdOX3u8/YP1Cf1B/yHrYfSRiNOnlybGjr7xf646zjS9M1L85Oen0VuId7t37qbbpizOH3mvNUs4OzhXPH/vg99FzwfdT0OfQL6GLoV/J3yK/x/yIWvJbNlyhXrn7U//ns1WX1U+/+tYpN8a2518MtEOm0CjCC4lBZqDEUL3oWIwUZh57DeeLl8KvErooLlNGEW2oZKmpqJdpXtK20JXTZzEcZfRhsmFWZxFhZWRdZ5tjH+Bo4qziKuYu4Mnlzd6TwZfMHylAEtQX4hH6Kdwtclk0TMxInFcCITEvOSL1RLpB5oZsnly8vJuCiiJGsVcpR9lJhVXlpepFNc+9suoY9QmNGs0MLV9tPR1BXRo9oPddf9Zg2PCBUa6xl4mAyaRpnpmlOda8zSLR0tiKxeqDdZNNlq2vnZo90X7C4abjEScTZ0bnNy5l+0Lg8391/8MD8Qd13XBu/aRC9wCPvZ6UnmNe170P+Sj7rPs2+8X7awWAgJbA40G6wajgjpATodqhPw9VkJ3hM7s83DL8R0Re5N7Iiaj4aM7ohzFusUyxY4crjiQedYoTjls+1hafddwnQS9RNInlBEUySP5xcirleWp12ql00in509jTY2duZaSdDcg0PEd37nHWvqyF7Ngc7Vyd8ykXcPlpBdMXWS/JXla5onJVoUiqWLiE9xprKe11Qhm+nBqOJPVKt5snq25Wv7i1fkf4rsu9c/f7axnqnOsLG0Ya0Q9Fmgyb3VuOPbrU2tT2pn3zMW+n7hOfp6e6bj8b7t7oEend13e+f+KF7ODpoc8jtqP1Y7yvcsal3lC9jZpOn4v5ZPFtedV6a/53vvdtFYwiAFlwnulwGq7zAGTWwnnmAwCYCQBYEQGwUwGIk1UAYVgFoIATf88PCE48cXDOyQS4gQiQhzNNM+ACZ83RIBXOKCtBExgA78E6RAeJQFpwfhgGnYbzwQ5oCgEheBE6CE/ESTjLG0D8QvIhzZGxyDLkCAqHUkUFoYpRL9F0aFM4I2vDQBgtTDymFYvGmmDPYkdxvLhAXD0ei3fEl+F/EcwJVwkrFBYUZZQoSnfKNqIAMZX4mcqOqhHOdDJpAM0hmmlaZ9peOgO6h/TK9DUMqgxtjDaMU0wRzBjmXBZBljpWC9Y5thR2GfYpjsuc7lxiXD+5H/Pk8HrukefD8L3ivyuQIRgoZCosJkIUWRQdEnsgfkkiTtJVSkWaQXpR5rnsDblUeV8FE0VJJUalTeVPKhOqA2pdezvU2zU6NXu0xrTndJb1gD4G3udwRjhjvAmlKYMZr7m8hYVlsFW2daPNjB3RXt7B2fGo0xXndpdZV4r90gccDh5xKyH1uP/05Pey9T7h0+j7y1834ELgarBHyMAhA3JjuHxEdZRE9O3YvYf7joYc44gfTshOMjuxfDI7VTyt45TXGcaMN5nPs8ZzNvN48lUKzS4dvBJTdKVk7LpE+ZVK6arJ21fvHailqK9q3N8s1srdYfCkqJuyV7h/eTBzRPhl/+tLb86/G3jvNr/6ie5L5TfwQ3pZZWVzNe1X3drg+oON4t+hm0rb+we0/c2BDrADQSALNIE5cAVBIA5kghJQD3rBDNiAmCApyATyhhKhIugR9A6BQgghzBBkRD6iDfEFyYE0RR5BViOnUWwoG1Q6qgMNodXRh9EP0OsYTUwi5imWBuuMvYb9htPGZeHe49XwWfgFggE85+sUThT34EyYTDlIVCFeoaKgiqaapXam7qExoGmh1aBtptOl66K3pR+HM9NfjBlMokzPmA+xMLHUsFqzvmeLYSeyl3BocUxzZnKZcFNxj/Pc5T2zx49Ph5+F/6PAQ8GzQt7COiIConRiOHG0BE6SSopOmlYGJ7MqOyc3It+l8EjxkVKX8iuVb2pUe6XVrTX8NMO1yNq+Ok66hnoq+vIGyoaGRgeN40yumnaaLVqwW+pbBcBnWrbtebsc+2yHK47NTl9dFPbFuz4/wHUw3K3Xnc/D2zPH6753j8+075o/U4BcoF1QZHB+SEvoBzJzmEF4ZMT1yLFomhjz2IzDo0cF444emzruk0iT1JUcnoJJPZmOOpVyhj2jLTMhyylH97zaBbUCtYsql0Wuoooel0SWsl9/WO5ewVg5XtVxq/fO0n2Z2iP1zxqpm/RayK2l7fOdOk/vdMv0FPaND/wY/Do8Ozo1Nvf6xxvoLWGKYYZ/1mg+d0HpS9r30pXA1Z61pPW2jR+/V7fnHwGvflrABSSABrAG3uAoyAW3QDf4AOEhMcgcIkN5UAv0AcGE0EOEI0oRY0hapDEyCdmC3ECpoWJRDah1tDY6DT2CEcEcx4xjNbBFOBwuBDeIV8FfJCAI/oQhCj2KB5QqlI+IVsT3VAnUvNQtNK40y7Rn6STontMHMxAZyhh1GF8zxTBzMfewnGF1Z9NhF+Vg4FjjHOeq4z7HE8Rrtkeaj4Ufw78q8FXwi9B34Q1RKjF+cS0JN8l4qYvSdTIvZL/LsykYKyYotalQqrqq3VLHwnfVJu09Oll6TPpVhi7GtCb9ZvkWIVb2NrK2Y/YuDt1ORs4v9nm7/jyQ6AaRQt2HPJW8Cn3wvsf9CQHFQeYhILSWHBLOFdEWFRHjefhzXEl8zPHhhPUkxAlcMs1JuZSw1MF0+1PzZ1LOSma+zErJUcv9mleef6CQcPH6ZaUrD4s0i1uu6ZV2lVmVD1bYVfZVGVTX3xa+c/4e7v7RmvW61AbBB30PE5oVW+ZbC9stH6M6HzwNeybWPd1zqc9pgOHFwFDGiMno5ljla8vxuTcRkxvvEqaRMwmziLnED6iPxxY+fzb4ErN48evpbxHf9b6v/LixZLH0atl3eXklcmX+p+vP3lXd1YpfxF+hvwbWFNby1r6uG68Xra9t2G3c/I387fS7chPatN+8sTX/Yd5ystvHB0SpAwB6YnPzuyAA2HMAbGRubq4VbW5uFMPJxmsAWgJ3/kPaPmtoACh8s4W6RIfi//1fzv8B7B3fj0cqVUcAAAGdaVRYdFhNTDpjb20uYWRvYmUueG1wAAAAAAA8eDp4bXBtZXRhIHhtbG5zOng9ImFkb2JlOm5zOm1ldGEvIiB4OnhtcHRrPSJYTVAgQ29yZSA1LjQuMCI+CiAgIDxyZGY6UkRGIHhtbG5zOnJkZj0iaHR0cDovL3d3dy53My5vcmcvMTk5OS8wMi8yMi1yZGYtc3ludGF4LW5zIyI+CiAgICAgIDxyZGY6RGVzY3JpcHRpb24gcmRmOmFib3V0PSIiCiAgICAgICAgICAgIHhtbG5zOmV4aWY9Imh0dHA6Ly9ucy5hZG9iZS5jb20vZXhpZi8xLjAvIj4KICAgICAgICAgPGV4aWY6UGl4ZWxYRGltZW5zaW9uPjcwMjwvZXhpZjpQaXhlbFhEaW1lbnNpb24+CiAgICAgICAgIDxleGlmOlBpeGVsWURpbWVuc2lvbj4yNTg8L2V4aWY6UGl4ZWxZRGltZW5zaW9uPgogICAgICA8L3JkZjpEZXNjcmlwdGlvbj4KICAgPC9yZGY6UkRGPgo8L3g6eG1wbWV0YT4KsjJseAAAQABJREFUeAHsnQecFEX2x9+Sc845R8kgRkBBMaCICphQjJjj6Xnq3V899c4cz5wwYALJCCioKFEyEpWcM0iSuP/6FvYymwi7s8uEX/EZZranu7rq2z3dv3716r2ERFdMRQREQAREQAREQAREQARinECOGO+fuicCIiACIiACIiACIiACnoCEr04EERABERABERABERCBuCAg4RsXh1mdFAEREAEREAEREAERkPDVOSACIiACIiACIiACIhAXBCR84+Iwq5MiIAIiIAIiIAIiIAISvjoHREAEREAEREAEREAE4oKAhG9cHGZ1UgREQAREQAREQAREQMJX54AIiIAIiIAIiIAIiEBcEJDwjYvDrE6KgAiIgAiIgAiIgAhI+OocEAEREAEREAEREAERiAsCEr5xcZjVSREQAREQAREQAREQAQlfnQMiIAIiIAIiIAIiIAJxQUDCNy4OszopAiIgAiIgAiIgAiIg4atzQAREICYIJCYmZqofBw4csMzWkakGpNiYtkRSe1I0L9mf0dLOZI3WHyIgAnFJQMI3Lg+7Oi0C0Ulgx44dtmnTJtu4caNt3rzZ/vzzz6SOjBkzxoYNG5amWESYse3evXuT1g/9MHnyZBs8eLBt2bLF+vbtaxMnTjSE8JEK61Dvvn37/Kq///67355lGS3U9f3339sDDzzg69q9e/cxVbVnzx7bvn17Ege25++Mlv3799sff/xhu3bt8lXQ5507dyaxnDdvnmcX9Jl3jhHvaQli6uF7WAffs+y1116z9evXZ7SZ2k4EREAEjoqAhO9RYdJKIiACkUDgpZdesuuuu87uvfdee+ihh+yNN96wlStX+qY1aNDAmjVrZgkJCamaigh7/vnnbdasWam+Y0HNmjWtVatWhsibPXu2rVixIs31Ui5EqL344os2Z84c/1W5cuXspJNOsrx586Zc9aj/ps4ff/zRKlWqZCeffLLlzp37qLdlxenTp9tTTz1l69at89t99tln9uabbx5THaErL1y40G699VZ7/fXX/cMAovXtt982Hha2bdtmP//8sxfFtHPZsmX2yiuv2F133eV5L126NLQq/4AwcOBAu+OOO/xxDER9rly5vJj+6quvkq2vP0RABEQg3ARyPupKuCtVfSIgAiKQFQQ+//xzO+OMM+zOO++0+vXr26hRo7x19LzzzvPWQiyRJUqU8AIMQfbbb795IYzF8p133jGsoYjSQOCuWrXKFi1a5JvKdwUKFPDCEUsyFuW1a9da0aJFvWUS0ZwvXz7Lnz+/F7qIaQTyRx995K2fiLdChQp5a3TJkiX9PhCH06ZN8wKxTJkyXviNHTvWNmzY4JcH7c2ZM2dSG8aNG2fffvutlS1b1po2berrnjJlihfktLtYsWLeWjpjxgzfT9pfvHhx3zYqKVy4sE2YMMHvgz7B7LLLLrMKFSr4fRzrfzDq3bu359uyZUvLkyePjRw50gtzxC7H4Oyzzzb69+GHH3pL78033+z7h4hv1KiRwYaCtRirO+v+8MMPdsUVV/j6gv5//fXXduGFF1rw97G2VeuLgAiIwJEISPgeiZC+FwERiBgCI0aMsFq1almLFi0M62rDhg3t1VdftXbt2tk333zjXRSw/CLUsNwynI444zVgwAAvghGlWEOffvpp7wKAhRiL7U8//WQnnniit2AicrFmIiBxPShSpIi9/PLLVr16datYsaLfJ6IYQYcIzJEjhxekiGEsrK1bt/b1IAQRt7hhIKBLly5tvXr18oJ69erVXrRXq1bNypcv7xkjuCdNmuS3pW6svuPHj7fvvvvOW7YRu/SbfT/++ONe3CKGYYLopiDsEZb9+vXzfb7ooousY8eOqSzhgcsC4pj286IulvM5KOxrwYIFvt88DGAdR8zDAhcKhDcPI3Bkn6eeeqqddtpp3g2F9WDBwwKFehHgPGDArXv37l748h3WX/qK2EfIq4iACIhAVhA4+BieFTWrThEQARHIYgIISSygDLEjbrEUIljxAW7btq1hoUS0IriaN29uPXv29C4NWFRLlSplV199tbccYxVds2ZNks8p7gq33HKLdzkYNGiQ1ahRw9cfuFEgStkfwpt1qRfBhsClDYg4BDDWy0svvdSwZL733ntesCP6zj//fDvrrLO8Hy/ikG1pY8GCBX27cRFgHay3CPbLL7/cC0jEOpZS+oKQvvLKK717R0rMtWvX9iIWN5BTTjklmZAN1sXyjKBG+NarV88LWrixLQ8PQcEPF8Zt2rTx7g08DNBHlsMaDvBA9NNv2kXhHd9dhHTKktYyxDF1YZ1XEQEREIGsInDosT6r9qB6RUAERCCMBBCfgQDdunWrtzoiYhFTiLEqVapYly5dvOUUv16sxFhSsWYGPqWsh1URiyqFv4N33BlwM2BIn3e2QxyGFobr2YbvsAgH9QbrsBxRiHWUgnUU6zP1UC9Cmu0Rh2wbKgSpmxfL6R+CmP4hNrFWIzCpBzGanvsCk/OwAOMOgssH9aUsuCG0b9/ei3Pahu8t71iUUxbahyDGsoxgRpzSHkQ8feWFpRkBjIWbwjtCNjhWoXXSJ5bzHhT6RD2BdThYrncREAERCCcBWXzDSVN1iYAIZCkBhBHCD0GI+CICA24CWCyxtiLQEIwIWiZQYdEcPny4t4oizJiYFYjgQCjTYD7zQowxfD937lzD6orLAwKSfSDSli9fbpUrVzYmfCGKEXa0ifZQL3XwN8urVq3qRSLiFyGKcAz8ixG9gXBmm9DC8qAe9ouYxBUDkYkFFxEd7Dd0u+AzbcTlAPcGhDGT7+CDZTq0YI2mbkowsY+/EbShhfYg7hGkuDBgcaYdnTt39iKZtnIsaBf7w8UESzhuGTyEwI9teNDA3xeBi8tEEN0Btwz6g98zxy49MR/aJn0WAREQgYwSkPDNKDltJwIikO0EsJBiwWTCFQIKqyoRHhCUCEOsoCwbOnSoF1cIKSIjIK4YvkeAIeJYH+tpYI1E1LEtwg+Bhuhl0hoW0HbOfxixi/8v4pqQZYhbXCiYSIewxaqMYGY/bI/VuGvXrt7dgTBdCD3cEhCJ7Jf9sG/6gzAM2gFQRCDLeQ/2i3vB1KlTvfjEh5Y+su9Qi2lwMBDZbI+LA++IVdqHXzR1BiUQvfzN59C/g3V4x0LNvvieBwpEMi4R/I2/M0KVSYQIX8Q2rhlE26CvuGjQxi+//NJzRPiOHj3a+/fyAAObHj16+GPDQwYWZdw7VERABEQgqwgkuKf5zEV9z6qWqV4REAERCCHApQrBiy8u4hVxifDCDYCCxRBBioAl2gLiDDGMWwHviFh8gdmObbA4MqyPhRNhisWW5YE1kvXZDsst4o/1Fy9e7C21+OIi0BCxWJERyohn2oMoxRpMvSxnIh37QcTSPiyyWHIR30wcY71QEU47aAP1I4oR77QbYY3wxK8Z0cg61JtSsNL3oI9wweWAiXTV3CS6lNZcvj9SoT2whA1txrrN37SD9s2cOdML33PPPdf7KGMN5hjBAB70H59qBDviGIb0G6b0rU6dOr4ewqVdfPHFnveR2qTvRUAERCCjBCR8M0pO24mACIiACHgxj4BFbKdlgeYhhRdCN63vQYh1GGGPFV1FBERABLKSgIRvVtJV3SIgAiIgAiIgAiIgAhFD4NCU2ohpkhoiAiIgAiIgAiIgAiIgAuEnEPGT2/AXY7IGw2hyRw7/CaAaRUAEREAEREAERCDSCKD5mGdBTPaMzE9Irz8RL3yZ6ctMamYopxWLMr2OabkIiIAIiIAIiIAIiEB0EmBiLpksmRgbV8KXWdCnn366XXLJJdF55NRqERABERABERABERCBYyJAfHBiqoe7yMc33ERVnwiIgAiIgAiIgAiIQKYJhMY4z3Rlf1Ug4RsukqpHBERABERABERABEQgogmEXfgSWJ2A7mn54waxGoPviO3IugR8VxEBERABERABERABERCBrCQQ1sltZBcaPHiwz67UunVrO+uss3w2o6ADOCl/9dVXdtlll1nLli19WtFffvnFZ/u56qqrfGajYF29i4AIiIAIiIAIiIAIiEA4CYTN4ov1FmHLzLsuXbrYggUL/CtoLCkzCUtGuk5SYC5atMimT59u3bp18+k7x44d67P7BOvrXQREQAREQAREQAREQATCSSBswjfIHU8u+YYNG/rYa6tWrfJtxcVhwoQJPtd7rVq1LHfu3D63O/np69ata7Vr17b169fbrl27kvpG/DYiOvBSEQEREIF4IMC1kmsexoENGzb40TOMBhs3bvTL+E7xzOPhTFAfRUAEsopA2Fwd8NvlgoyoZRZerly5kkTrwoULbfbs2daiRQsjp3twEc+bN6/vF+sGF/ygozNmzLARI0bYzJkzrWvXrsFivYuACIhAzBDYvHmzF7jz5s3zYXsYEUPwYkjgmsgrmNXMtbVIkSJWpkwZq1KlitWrV8/q169vxYsXt0KFCsUME3VEBERABLKSQNiEb8GCBb3Y3bp1q+3Zs8dbb4sVK+bbjhvEunXrvE/v5MmT/Xpt2rTxApgLO9sgggMhzEZYhsuWLWvDhw/3F/+shKC6RUAERCC7CBCbcv78+ca1kOQ8WHR5+C9cuLC/5nHtQ8zyd5CxEgsw10mMBmvXrvXbDxgwwBsaqlev7gO8t2rVymrUqGF58uTJrq5oPyIgAiIQdQTCJnzz58/vXRwGDhxoU6ZMsQoVKviLOZZbLuTPPvust2I899xzdsYZZ/hMbFiBn3jiCSM7R/fu3ZNNhMOCwatcuXL++6gjqwaLgAiIQAgBJv8OHTrUP8yvWbPGEKyI1Tp16ljNmjWtYsWK/hqYI0cOb+XlPbRgJAhcwLZv324rVqwwLMVz5syxvn372ptvvumvtR07dvQTi0uXLh26uT6LgAiIgAg4AmETvtBs3Lixtzbgr4vvLmIY1wYsEAzTYdG9+uqrjQsyFmKiO3DhxrLRtGnTNA8IF3sVERABEYhWAkuWLLHPPvvMu24xGka0G7JRMrcBsYu192hKkLKT9bmWMkeiSZMmfnQNEYyRYfTo0fbyyy9bnz597IorrrBzzjnHSpQocTTVax0REAERiAsCR3fFPUoUCN1mzZoddm380oKCnxovFREQARGINQK4JPTv398+/PBDL1SJdoMQrVq1arLRrcz2m+suIppXhw4dbPHixfb11197Ady7d2+78cYbvdguWrRoZnel7UVABEQg6gmEVfhGPQ11QAREQAQySQCr7siRI+3FF180Jq9heeXFnIXAapvJXaS7OfMqMD40atTIh5X8+OOP7fHHH/dC+G9/+5s1b9483W31hQiIgAjEAwEJ33g4yuqjCIhAthDAdevRRx+1adOmebcu5i4wxyG7C+4QiFxE8NSpU73VmSRBF154od13333e3Sy726T9iYAIiEAkEJDwjYSjoDaIgAhENQEi1zDB7Omnn/aT1j744AMje2VWW3iPBI1QaISRJLY67Xv++ed9IqHHHnvMiKyjIgIiIALxRiD5tOF46736KwIiIAKZJMDEsrvuusv+7//+zzp37mz41Z5yyinHXfSGdouwaFh8SSlfrVo169mzp73++uvJkgaFrq/PIiACIhCrBGTxjdUjq36JgAhkOYFff/3V7r77biM2L9bUTp06Zfk+M7MDMmu+++67/vXkk0/6UGiPPPKIDxuZmXq1rQiIgAhECwFZfKPlSKmdIiACEUOA1MFMHOvRo4cP3UgUhUgXvQE83C969erlI04QS71bt24+DFrwvd5FQAREIJYJSPjG8tFV30RABMJOYNeuXd6Xl6Q8l1xyiT3zzDOGJTXaCr6/iHcSaNx5551eCCPoVURABEQglgnI1SGWj676JgIiEFYCJOf53//+Z4MGDbIHHnjAunbtmizVelh3lg2VIdgJu/b222/bQw89ZPQPKzaxgVVEQAREIBYJSPjG4lFVn0RABMJOgElsWHnHjx/vQ5add955R511LeyNCWOFZM684447fDrkV1991aeWxxWiQIECYdyLqhIBERCByCAg4RsZx0GtEAERiGACTGL7z3/+Y5s2bbLnnnsu5kKBkVb+3nvv9aHYcN3YsmWL3X777Yr3G8HnpJomAiKQMQISvhnjpq1EQATihAATwMh+tnfvXnvqqaeOmJY9WrHkyJHD+ywXLFjQnnjiCW/5veeee6xixYrR2iW1WwREQARSEdDktlRItEAEREAEDhKYMWOG/fe///UxeRG/ZEKL9dKxY0e7//77bcqUKX4S3/Lly2O9y+qfCIhAHBGQ8I2jg62uioAIHB2BxMREmzBhgrf0YgnFzaFRo0ZHt3GUr0W2N1IbE+d3yZIlPjHHsmXLorxXar4IiIAIHCQg4aszQQREQARSEJg6daox0Stv3rze95VsZ/FUEL9kn8PVYc2aNT7L28qVK+MJgfoqAiIQowTCLnwPHDjgfeGwmIQW4kPiIxcaJzJYxvKU64duq88iIAIikF0E5s2bZy+88IJxLSNkWZMmTbJr1xG3n3bt2nnhj9vDK6+8YqtXr464NqpBIiACInAsBMI6uW3z5s02duxYbyHAF65x48aWO3du+/PPP30IoKVLl/r4kK1bt7by5csb2Y62bdtmhQoVsjPOOMMvO5bGa10REAERCCeBhQsX2muvveYf0hG9TZs2DWf1UVcXlt8zzzzTuLYT6/edd96x2267zUqWLBl1fVGDRUAERAACYbP4Bj5xzIAmLuTo0aMNoet34nzkypYta/Xq1bO1a9fa0KFDfW571ilevLhP+ZlezEj861REQAREIKsJLFq0yCdzIF7vww8/bC1btszqXUZF/VyDu3Tp4sOb/fTTT97t4Y8//oiKtquRIiACIpCSQNhU5Y4dO2zVqlU+/SU56/Ply+cnRiCIiRGJjxzLdu/e7YO+Y0nIlSuXH04kfE5K4YtfGYHimVXNuioiIAIikFUEGMJ/9913DfF78803x7V7Q1qMuVafc845duWVV9oPP/xgffv2tZ07d6a1qpaJgAiIQEQTCJvwxZ0Bn10EbM6cOf2kEHLaB767COP58+d7iy/DZIhgXB4QuF9++aUPnROsCzEsCgsWLDAmVEj4RvQ5pMaJQFQTwN0K0Ysf60033WTt27eP6v5kVeOZ6HfppZf61+eff24DBgywPXv2ZNXuVK8IiIAIZAmBsPn4clFkSAyxiwDmgogIDlwVSpcubd27dzdyw3/zzTfeetCzZ0/fKS6iWHZbtGjhfYJZWKdOHf8qU6aMLAuekv4TAREINwGuU/3797cxY8Z4ayZWTeYlqKRNgPkYl19+uTdIfPzxxz6zGw8KwXU+7a20VAREQAQih0DYhC8XxCpVqhhhgLZv3+5dGooUKeIturg6MFMaN4e5c+f6iRFYdOfMmeOzAxEjEqGLpThlYWa1igiIgAiEmwDXo0GDBlmfPn2sa9eu/sGckSiVwxMoVqyY3Xrrrfbyyy97f18eFNq1a3f4jfStCIiACEQIgbC5OuCO0Lx5c6tVq5Zt3LjRx4Bk4hqzgQlXxqQ2RG/+/Pl9cHRE7uLFi43JcER4IGakrAYRclaoGSIQ4wQYlZo4caJ98skn3p8X4cu1SeXoCFSoUMGuu+46Pzn5/ffft99+++3oNtRaIiACInCcCYTN4ks/SpUqZRdffLGfsBZYb/HbRRSTCSj4zHd8xl+MdwSvRO9xPhO0exGIIwKzZs2yN9980w/V9+rVywu4OOp+WLpat25dg93zzz9v7733nt11110KSRkWsqpEBEQgKwmEzeIbNBIBywxgxC4v/uYdscvyQBCHLpPoDejpXQREIKsJrFu3zsekZUIuMWlr1KiR1buM2fpbtWpl119/vZ8Y+MUXX3jXtZjtrDomAiIQEwTCavGNCSLqhAiIQMwS2Lp1q33wwQe2fPly+9vf/mYk2lHJOAGMFh06dPCT3ZikXKJECevWrZuP2pPxWrWlCIiACGQdgbBbfLOuqapZBERABDJOgAgOQ4YMsREjRliPHj3stNNOy3hl2jKJAKN4uLjBE6svSS5UREAERCBSCUj4RuqRUbtEQATCSoCEOL1797Y2bdoYSXYCt6uw7iROKyPSQ08XnrJixYo+JrImu8XpiaBui0AUEJDwjYKDpCaKgAhkjgCuDW+88YaPI45PaspMkZmrXVtDgHCWJADZt2+fffjhhz66j8iIgAiIQKQRkPCNtCOi9oiACISVwIYNG+ytt94yJrPh11u5cuWw1q/KDhFo2bKl3XnnnUmh4sjYqSICIiACkURAwjeSjobaIgIiEFYC+PX269fPfvjhB590oUGDBmGtX5WlJnDqqada586dfXKQH3/8MSltfeo1tUQEREAEsp+AhG/2M9ceRUAEsonAzz//bB999JGdf/75duaZZ2bTXuN7N4StvPLKK+2EE07wsZIXLVoU30DUexEQgYgiIOEbUYdDjREBEQgXgSVLlviUuvXr17drr73WxxEPV92q5/AECGuGvy/l448/ti1bthx+A30rAiIgAtlEQMI3m0BrNyIgAtlHYPv27fbMM8/4hAr/+Mc/rFy5ctm3c+3JE2jYsKHde++9NmrUKJ8aGh9rFREQARE43gQkfI/3EdD+RUAEwkqANOh9+/a1CRMm2AMPPGA1a9YMa/2q7OgJtG3b1i666CIvfBXf9yA3/M537doVV77P9Hf37t1Hf+JoTRHIQgLK3JaFcFW1CIhA9hMgXi+hyxhqJ2avyvEjQGp63EwWLlxor732mn8IiYcU0USzmDt3rg/plidPHqtVq5aPJrJz506fRIW4x/ic4w9NYf1ly5b5kHAFCxb0EUhgVq1aNePvjBSimcyfP9/YP+4+hQoVSlUND4lLly71xyd//vyGlb5o0aJ+PcLSsT3bVapUKSnu9d69e23mzJl+WdmyZf26tH3evHlWpkwZa9q0aar9TJo0ye+DxDG5c+dO9X1GFuA+M3v2bM+QSauFCxdOVc3atWt9W0uWLOmzNHI+rlixwogzzQgE/Em7zfFQiR8COR91JZK7ywnKD1CzsSP5KKltIhAZBFauXGl33XWX1alTx3BxyJs3b2Q0LI5bgaBiotvQoUNtzpw51q5dOy/GYhnJggUL7Mknn7Rt27bZqlWr7LvvvrNSpUr5v4l0ccYZZ/i/AwYIYh7WVq9ebU2aNLE+ffp4FxHCw4UK3/379xtpoo9UELRTpkzxCVsGDhzo66xQoUKyzVjn+++/99b4TZs2+bbhEoR/NgVxe/PNN3vrdIsWLZJ+S9T397//3RC9jRs3tsmTJ9uLL75otI1jjIhv1KhRsn0VKVLETzKtV69esn4nW+kY/ti8ebN/kPr111/9/hcvXmx169Y1zrWgsOzf//639y+nn6Qrh+0777zjR4QQ9H/88Yd/KElLNAf16P34EWCUgN9L+/btkx4Sw9GaI/+CwrEX1SECIiACWUyAG+9LL73kb7y4OChJRRYDP4bqq1atarfffruNHTvWhg0bdgxbRueqBw4c8H7lN9xwg91xxx3eyolARPgjzhDBoQWLIyHgEKuffvqp50QkktKlS4eu5uMjwxEhjcUS8ZpWwbLZvHlzu+222wzBS3tSFsQjghDxevfdd9t1111nHCcK1uKJEyd6ccvDY7AfHixxWcGCjACnXtrCdvfdd59dccUV9v7773uxHLo/rMiI6mnTpoUuTvWZ3zCuIKEvLMzB/oMN4LRx40YjGQ3ifMaMGcZk1qDQrtGjR3sr9cMPP+z79sknn3hmrBPEm77lllusfPnywWZ6jxMCYXV14ORcv369f7LiZAqGVjiZGXLg6ZcfPd8x3MFTLj8klvHjPJon2Tg5LuqmCIjAMRL44osvbPDgwfb88897688xbq7Vs5gAVpurrrrKXn31VW9la9asWRbv8fhWj+UTiyTCEWsjYhfrLxbcfPnypWocVlXWx1KMIDvxxBMNARtaEKncS7/++mtvuYQpL+6fodZOtuH+i+tBeqm5A1cBshqOHDnSateu7d2DqIswgIy0IhC5V9MO7uNfffWVd2XAtYHCPR//3eLFi/u/EbhYrXGfwLobFLZHHGMJT69gfUWcjhgxIqnNtAG9gDBHbAcFay5948EAazJthEtQaCvrYOHFnYG28E67WP+zzz6zqVOn2kknnWTXXHNNqgeMoB69xyaBsFp88Wl64YUX7KmnnvJPrZzIFH4Yw4cP90M5zz33nH9C5Imud+/e9vTTT/v18Q9SEQEREIGMEODm/d///te6dOli5557bkaq0DZZTADh0bNnTy/8GBqP5RBnCD2MOm+//bZPoNKxY0c7++yzvZjEwJOWGIUPgph3BF1avrCIWc7x119/3d83mcCJ28SQIUPSPHppWXqDFbkvIxZxI0Rs0yZcFbgX49t71llneSst7WH0ZMyYMX5T+oJrAIKebUhYQjsIW0fMbPqOlTZlwdeYfaZXEKS33nqr4UqBsOc1aNAgn3UxVPSyPfoBPrDkRRtDLeD0m3WChwHaRHvRJFjWmfwKQ4T4559/7kV9eu3S8tgjEDaLL74Yv/zyi/ftYZjxgw8+8I7nPFHxY2UYhcIPlCEfhnYYTuECiA/HuHHjvBWAH4eKCIiACBwtAUaSuOZg1WFYUyNHR0su+9fD6omxAwGMW8q//vWvmDxeWELxOcVSGUzmQ4xhESXUHqIMsRZauC/iCnL11VfbDy7TIK4KoVbTYF0eGBCohIlDLD7yyCN+4lbwfeg7gi+9gijEysvkrmpuEh0CmAl13KMxVGHI+v333/3xwe8XKzCiGN9fLNOIdPqGoMf6On36dDvttNP8e/Xq1ZPtFh74ER8urCC/YyzK9Ct4MMDiyza4M+C3HxQszOgHOGJZR3/QxqC/sEVjrFmzxm/CenDDekxbg0LUkVmzZnlBHoxQB9/pPXYJJP/lZaKfwcmHwztPhzwRcmJywnMyLnH+Nx9++KH/wTCMs27dOu8/hNDl6ZYfGE+DgfDliZGTHncI3cgycWC0qQjEOAGsTDx09+/fP8m9Ksa7HNXdC3xKibN88sknGxbEWCvc97h/hVo4uQ8iFBG3iN9QH3RcIRh+x92ByAe462DxxAIaGnGA8/zxxx/3w/4XX3yxnzSIaE2rIAZxPWRf+MNyj0bsshxhSKQDojUguHkgQdDSvlNOOcW7COAugGWUguhkwhpWbOqhbwhNhCSClboIW8dDzXnnnZfqd0hdTFSnzekVhDTCmTYEAhaOtDmIHhFsS+QIDGa0HUHNthUrVvSWW/rHNgh6Jgxi1cWVAzGOGwcM0RzU/e2331rr1q2THYtgH3qPXQJhE75pIQpOXr6rUqWKD2bOicaTZOhTF9+nFLf43zAEwUnLBAEVERABEUhJgJvYs88+668tKWeSp1xXf0cOgcsvv9yP8v3nP//xlk2ESCwV/HgRcKHilvshQ/a4BeB/Sp+DeyTWUsQdbjoYf7CI4wtN6K1Q4YufLJZyBCtD94crCEMeLnABwMUQ31vcJLDosi9cGRDZ7733nj322GP+IeSCCy7wghZLMAXRjMglzBlikt8YlmsEPXXwoi+IccT16aef7ifzpWwXhi2suDz0pFdwXUBgh1p201sXjpdccon3CYbhjTfe6EPlMXkQa/lll11m7dq18xZfkqigP+gjOoPQali02R/Was7FlPojvf1qeWwQSHBPPWlPCz3G/vGUxeQSTkJ+UMxM5emNpyme9vixcKLh0jBgwADvZ8OMUqy/zBLlqY2JD4HFN9g9ju78+DjJVURABEQgIMCsdGaRM+z5oRtNSnntCNbTe2QSYBQQ0YHYuv/++9P0aY3Mlme8VYhILKuMaGLdTenukPGaI3tLojDgboDrYyD2I7vFal0kEMAnmwcW5o0d6UHvWNobNosvjWIGKMM1iFs+8xTFUARPtjipMwEFEUzgboYh8BPCxwtBTLD5tG5cXChUREAERCCUAA/STzzxhHenevPNN9O8doSur8+RR4Aheo4hw/n4lzJUHusFoYvvbrwVRL6KCEQKgbAJXzqEIz4XMfyV8LfhyY4nW/xvLrzwQu8bxNAP3yF2r7zySp9ZiWGhypUrRwoTtUMERCDCCTCMS+gyhsqD2KMR3mQ1Lw0CRCRgeD9weWBIWkUEREAEspJAWMOZYeHF2R0BzOQ2ZkkyDIlvEDcnnup5ykf0UvgeXx0udhr+yMrDrLpFIHYIEEMU38WuXbv6iTSx07P46wn3DCJycL9gOBN/VBUREAERyEoCYRW+WdlQ1S0CIiACuD4RG5VRJSa08FCtEt0EmGlPClzmfDChWUUEREAEspKAhG9W0lXdIiACYSXQr18/H8P0wQcf9KNHYa1clR03AkyIZp4H0QeY+6EiAiIgAllFQMI3q8iqXhEQgbASYDY8cTk7deoUk7FfwworCisjyREpZgnXFWT9jMJuqMkiIAIRTkDCN8IPkJonAiJwMO35yy+/7H1BsQyGM7SN+EYGAeaD/O1vf/NxbsngpSICIiACWUFAwjcrqKpOERCBsBEg1Pg333zj06WSupSoMCqxSaBZs2Y++QBJFeTyEJvHWL0SgeNNQML3eB8B7V8EROCwBMjG9L///c9HcSDTkrIsHRZX1H95xx13+ChATz75pI/THPUdUgdEQAQiioCEb0QdDjVGBEQglAC+nm+99ZZP20r4siAUYug6+hxbBIoWLWp33323T4X7/vvvW5iSi8YWJPVGBEQgwwQkfDOMThuKgAhkNQEyPk6dOtWuvfZauThkNewIqp/sZiQ4+vrrr/3xj6CmqSkiIAJRTkDCN8oPoJovArFKYPbs2da7d2/r3LmzT3Meq/1Uv1ITwLJ/1VVX2cknn2zPP/+8rV27NvVKWiICIiACGSAg4ZsBaNpEBEQgawng4tCnTx8rXbq0XXzxxUaqc5X4IkCUh2uuucaWL1/uE1vs378/vgCotyIgAllCQMI3S7CqUhEQgYwSwKdzyJAhNm7cOG/1q1mzZkar0nZRTqBx48Z+UmPfvn19mLMo746aLwIiEAEEJHwj4CCoCSIgAocIEMXhs88+s9atW9vpp59+6At9ijsCRPBgUmPt2rX9JEdSVauIgAiIQGYISPhmhp62FQERCCuBTZs2eYFTpEgRP6GtcOHCYa1flUUfgfLly9utt95qq1ev9u4ve/fujb5OqMUiIAIRQ0DCN2IOhRoiAiJAFIe5c+f6JAa1atUSEBHwBHB5uPTSS23AgAE2adIkUREBERCBDBMIu/Ddtm2brVu3zvbs2ZPUKHz2GKJas2aNbdmyxQ4cOOC/YwILs3V5/fnnn0nr64MIiED8EZg/f76Rqhb3hjZt2ljOnDnjD4J6nCaBPHny2EUXXeQnO77zzju2fv36NNfTQhEQARE4EoFcR1rhWL5n9u3QoUP9kFSrVq2sffv2lj9/fkMMM1ll6dKlxgXsrLPOsiZNmtgrr7xiu3fvNgKWE7IIPy4VERCB+CPANQK/XlwbsOxxTVARgVACZcuW9ZMdn3nmGfvyyy+tV69elitXWG9hobvTZxEQgRglEDaLL6FmJk6c6K25nTp1snnz5tmCBQs8NmIynnTSSdajRw8rV66cfffdd8b6COFzzz3X+/JVqVIlTcS6sKWJRQtFIGYIMCJEooKxY8daz549rV69ejHTN3UkvATatm1r3bt3N6I8/Pjjj+GtXLWJgAjEBYGwCd/t27d7NwYE7AknnGAFCxa0VatW+XSTWH0JSVS5cmUPNUg7yg3vm2++sVGjRtnOnTuTAUc4v/3229a/f39jZq+KCIhAbBKYNWuW/523bNnSTjvtNP3eY/Mwh6VX3EswrOD//eGHH9rGjRvDUq8qEQERiB8CYVOUzLTFdxdRm5CQ4P3z9u3blyzP+oQJE+y3337zPnz4711//fXWoUMHW7lypX377bcWOlu3RIkS1qJFC3+BQyCriIAIxB4BfP4/+eQTy5s3r5/QVqhQodjrpHoUVgJEeSCr24YNG/xIQTBnJKw7UWUiIAIxSyBsDlJYeBG9TFhjYhsW3GLFiiVZb4jNOWbMGOvYsaM1a9bMC2LSUVIQvDNmzPAT3AJrcJkyZYwXE+VSWoNj9mioYyIQRwR4oB0xYoRNnTrV+2s2aNAgjnqvrmaUACOAJ554op133nnWr18/P1+Ev1VEQARE4GgIhE34MgRVv359P7kNEYtoZSIbgpeYnC+++KIRo5OLFkKWyW24OBDpgRe+W2mlJdXT/NEcRq0jAtFHgCgOn376qXdv4IE4eOiNvp6oxdlNgPsNiS2mTJlib775puFix/wRFREQARE4EoGwCV92hJhF7BJqhgkqXJyw5vJ+5ZVX2q5du/wsXC5QLKtRo4aRj50IEGyr8EVHOlz6XgRigwBzAvr06WP58uWzbt26+Yfj2OiZepFdBLiP4PLw1FNP+TB4JLnQPSS76Gs/IhC9BMIqfBGzzZs3T0WDIc127dqlWq7hqVRItEAE4oLAyJEjDZ//m2++2erWrRsXfVYnw08AdzlCYQ4ePNgbT4j/rCICIiAChyMQtslth9sJk91UREAERAACCxcu9HFYGRU688wzZaXTaZFhAswtufDCC40Jbx9//LFPlJThyrShCIhAXBDIFuEbFyTVSREQgSMS2Lx5sw9DRabGG264wU+APeJGWkEEDkOgevXqdt111/m48F988YURTUhFBERABNIjIOGbHhktFwERCDuB0aNH208//eQnJjVq1Cjs9avC+CTQunVru+CCC2zgwIF+wlt8UlCvRUAEjoaAhO/RUNI6IiACmSawbNkyH7OXcIYkIZALVKaRqoK/CDBJklTXxIF+//33fQQhwREBERCBtAhI+KZFRctEQATCSmD37t0+5irD0ER4KVq0aFjrV2UiECS2IEnSoEGD5PKgU0IERCBNAhK+aWLRQhEQgXASIGb3119/bVdffbXPyBjOulWXCAQEiAdNYovevXvbxIkTg8V6FwEREIEkAhK+SSj0QQREICsILFmyxCeqaNiwoZ1zzjlyccgKyKrTEyCO/GWXXWYVKlSwd999Vy4POi9EQARSEZDwTYVEC0RABMJFgKQ1X375pa1evdrPvC9cuHC4qlY9IpAmgUqVKtk111xj+JQPGTLElP0zTUxaKAJxSyCsCSzilqI6LgIikIoAgmP48OE+jTmhy5SwJhUiLcgiAsSHxteXlNi1atWyU045JYv2pGpFQASijYAsvtF2xNReEYgSAlh5SUtMZjZCTamIQHYRyJUrl3Xp0sVPoiS27/r167Nr19qPCIhAhBOQ8I3wA6TmiUA0EiBBRd++fe2PP/7waYmLFSsWjd1Qm6OYAH6+uDxMmzbNuzzs3bs3inujpouACISLgIRvuEiqHhEQgSQCkyZNssGDB/uJRk2aNElarg8ikJ0EcHk466yzfCi9yZMnZ+eutS8REIEIJXBUwnf//v2GBYcXn1VEQAREID0CRHF44403rEaNGtatWzfLmTNneqtquQhkKYH8+fPbtdde610e3nnnHduwYUOW7k+Vi4AIRD6Bw05u27Fjh61atcpWrFjh38m0xPBR5cqVrVy5clawYMHI76FaKAIikG0ESFSBiwMC45577tE1ItvIa0fpESDKQ48ePeyFF16wb775xrp3726EPVMRARGITwKHFb6//PKLjR8/3vLmzWtlypTxYWGmTp3qc6GfdNJJxivUmkPoojlz5viJBExoqVq1quXIkcP27Nljv/76q1+OWCaeZ/HixW3lypV+OekmW7Ro4dNNxudhUK9FIDYIcH0YOHCgXXXVVYriEBuHNCZ60bZtW3+v4aGM+0/z5s1jol/qhAiIwLETSFf4JiYmWsmSJe3666+30qVLJws6v3btWj9phfSjocJ3xowZPnQRzZg3b57378MyjOV47ty5xnZYgtasWeNneffr1882b95s27dv9+kl8cfCqqwiAiIQfQR4kP3oo498FAdcHFREIFII4PKApfenn34yojxUr17dG18ipX1qhwiIQPYRSNfHFwHaqFEj3xIuFLg8EBJm2LBh3qpbu3ZtbwkOmoq1F3HbuHFju//++72AnT9/viGgixQp4i869957r4+nuGjRIr8uoveuu+6ySy65xGbNmuXFdFBf8I7FWEUERCCyCfBwi+jlgRcXB0Z0kkqi+xS8khbqgwhkLwFc9Hr16mWMZA4YMMAbW7K3BdqbCIhAJBBI1+IbNA5fKATqq6++6oUuT84XXXRR8HXS+86dO41wMYhctmE9QhkhfAOr8Lp162zBggVWr14927JlixHiCGHLO76BTJ4rWrSor5N1ly5d6oenatasmbQffRABEYgsAiSqGDdunA8ZRbpYhpJVRCASCXTo0MEL36+++sq76tWvXz8Sm6k2iYAIZCGBI5pT8e9lQhsuClhz+Iy/b8pCwHCsxPjzInaJ/oAADiy2iGAmFuDj265dO+/Pi9ClsA3iOBDILNu0aZPNnDnTFi9eLPcHgKiIQIQSIDXsu+++60eILr/88tStxHspeKX+VktEINsIcE+6+uqr/f3n888/90adbNu5diQCIhARBI4ofLdu3Wq4JjBZ5b777vOW2unTp6dqfKFChfzwJjdBfH0Z+mS4k3cELv68LMd9AgtRlSpVvG8vk+FwcyhVqpQVLlw4qV6swvgXd+7cWbnWk6jogwhEFgH8/MnOht8+w8j8jlVEIJIJ4N/L/Qx/31GjRilEZyQfLLVNBLKAwGFdHfDpxWWhZ8+eST57RGvAGssLt4TASst769atvQ/wiBEjrFWrVt66u3DhQr9eYLn9+eef/bbnnXeet/x+9913vo6uXbsm8xkO+sqNVUUERCDyCDCy8+OPP9qgQYPszjvvtGbNmkVeI9UiEUiDwLnnnmtjx4613r17W61atYwkK5pYnQYoLRKBGCRwWOGLZXfjxo3etSGwxmIBxj+3fPnyXtwGwhc2TB7gSRoLL+tzIcHlgXWwFvMZay/uE7hAtHMuD02bNjXcJPANVhEBEYgeAvjgv/XWW37CKiMzKiIQLQRy587tE1s8+OCD9vHHH/sRyBIlSkRL89VOERCBTBBIV/hizSH8GCJ39uzZ/sIQiFZ8fInRi79UyoIPb2hiCy4wlGDSWuj6CGJCpqmIgAhEFwEms77//vv+GvHkk08m+81HV0/U2nglgDvdDTfcYP/973/9qAW+v8GclHhlon6LQDwQSNfHF+G7fPlyfyHYtm2b991DpOKby5Am2XBUREAE4pPA6NGj/WRV3KAIbagiAtFIgCgPvD777DM/eTsa+6A2i4AIHBuBdIUvT76nnXaaF78MaQYvMjMRkkxFBEQgPgmQhfG5556zjh072hVXXBGfENTrmCBA1tBbbrnFu/O99tprRhhNFREQgdgmkK6rA90+9dRTveP/ihUrjHiHuDrgtxu4L8Q2GvVOBEQgJQFcHF566SXvw3/zzTenOSE15Tb6WwQimUDZsmXt1ltv9YmXvvzyS7vpppvSdOOL5D5EZNtIWhMUJWQNSOg9AggcVvhi9WUSGy8VERABEejfv79NmTLFnn/+ebk76XSIGQJEJCIx06effuonXDPaqRJGAohgid8wAlVVmSGQrqtDZirVtiIgArFHgOxsL774ot12220+Ikvs9VA9ilcCGHmY6NayZUt79tlnjTCcKpkkECStCd4zWZ02F4FwEZDwDRdJ1SMCMUyAtOVYeatVq2bdu3fX7PcYPtbx2rVixYoZ7jtEMnrvvfds79698YpC/RaBmCYg4RvTh1edE4HME8C3/80337QlS5bYP/7xj2QZFjNfu2oQgcgh0LBhQz/ZbdiwYfb9999HTsPUEhEQgbARkPANG0pVJAKxSWDo0KE+3BPZ2Vq0aBGbnVSvROAvAhdeeKGR2Y0RDjKOqoiACMQWAQnf2Dqe6o0IhJXAokWLjAQVnTp1sssuuyysdasyEYhEAgUKFLB77rnHZxx97LHHbPv27ZHYTLVJBEQggwQkfDMITpuJQKwT2LFjh7d6EdWFWKekGlcRgXggQHbSBx54wEcw+fDDD+Ohy+qjCMQNAQnfuDnU6qgIHBsBQjuNHz/e7rvvPqtcufKxbay1RSDKCbRp08Y/8L311ls2atSoKO+Nmi8CIhAQkPANSOhdBEQgicCkSZPs7bff9u4Np5xyStJyfRCBeCFAiLOrrrrKhzj797//bZs2bYqXrqufIhDTBCR8Y/rwqnMicOwEiGH6r3/9ywjq36tXL4UuO3aE2iJGCBQpUsQef/xx7+bD++7du2OkZ+qGCMQvAQnf+D326rkIpCKwZ88ee+WVV3wMUxJVFC1aNNU6WiAC8UQAN58HH3zQRowYYf369YunrquvIhCTBMIqfIn3uWrVKps7d6798ccfScASExNt7dq1fvmGDRuM9SgrVqyw2bNn25w5c2zbtm1J6+uDCIjA8SEwYMAAGzNmjN11113WoEGD49MI7VUEIozAGWec4RO3PPPMMzZjxowIa52aIwIicCwEwip8582bZ6+//rq99NJL9sUXXySJX6xIBANnkkzfvn3tzz//9G385z//6dft06ePLV++/FjarXVFQATCTGD69On+93j11Vfb2WefHebaVZ0IRDcBHgbr1KljjzzyiK1bty66O6PWi0AcEwib8MX3afLkyVa3bl3vE4UF99dffzWsvblz57bOnTvbpZdeaoUKFUqy+LKcTFBPPPFEutalnDlzxvHhUddFIHsIrFy50h599FH/+73uuussX7582bNj7UUEooRA8eLFfUzrrVu3GkabwIATJc1XM0VABP4iEDbhS8xPLgSlS5f2foEIXGbBInyZHZs/f35/M01ISEiCv2/fPu87RZBwbryhhTBKPGG//PLLmlwTCkafRSDMBPgdMkqzefNmH7hffr1hBqzqYoZA7dq1/T1r3Lhx1r9//5jplzoiAvFEIFe4OovApYQK25R1B+sEy0kJidWXCQMDBw60UEtTq1atrFmzZkbO9MAnONhO7yIgAuEjMGjQIBs5cqQfeTnhhBPCV7FqEoEYJHDOOefY0qVL7amnnvKuD0rjffAg79q1yxu40jvkzPvZu3evlSxZMs1VGDVmLhAJc9AF4Shr1qzxxrgjjRzz8L9x40YrW7Zsst2iWUJ1C/rmcBon2cb6I2IJhM3ii4WXzE7r16/3E9U4ybH+Yu0NCidfrly5/Asxy9AR2zFrlh8NP4qgsB7DrcoWFRDRuwiEn8DUqVO9Xz7piNu3b5/s9xr+valGEYh+AtzTrrjiCmvUqJER35d7XryXsWPHGqmeEa4py+DBgw1LebFixaxUqVJWsWJF+zBFNjyy5BUuXNiqVq3qhXFmo2fwIM9+ENGEpCPteloFUXv//ff7Uepy5cp5LTJhwoSkVStVquRTV6NdeJ166qlJ3+lD9BI4pEoz2QcEKlZa/HqDE4mTiiEhRDDDQu+//76/yZIJhycxhlfvvPNO++qrr/wJhQhWEQERyB4CWK2ITcoFn3i93LhUREAEjkwAdyB84rm38RvCcBPPJRiVDd4DFqNHj7YLL7zQOnTo4KM3MQH+oosusmuvvdaGDBniV0MjPPvss/bJJ594nojizBi88MFmH127dvXulowsMyGRpDwpCxPrcaf88ssv/bqMMl9++eVJq+HC+d5779nMmTP96/PPP0/6Th+imIATp2Er7qRPdLNdE10A/MTt27cnupMm0Z2EiW4YwS//7bffEufPn5/owpglukgPic6vN3HBggX+7/3796fZDvfjSHSRINL8TgtFQAQyRmDLli2Jd9xxR6KL3pDoJqVmrBJtJQJxTsDF9k10YinRibVE7n/xWlwIRHwdE10402QI2rVrl+ispMmW8UfLli0TXYg4v9yJTr/tokWLUq2XkQUcizx58iTu3LkzaXNnuU186KGHkv4OPpx//vmJF198cfBnohPhvi0uwo1f5h5wEn/44Yek7/UhewmgH++9995EN38srDsOm8UX7Y/vC+4NNWrUsIIFC3oLEsMMDBGwvFatWt4niiEIfHgqVKjgh0D4O9QlIoqfI9R0EYh4Avizvfvuu4abg7uoWNOmTSO+zWqgCEQiAeL73nLLLX4kkwQXKskJcI3p0qVL8oXur/POO8+w/lLatGnj3SBwtWL0N6XV2K/k/uvWrZv3wcUPN3ihIVJm03MC2msNJtQHpV69ej7HQPB38E6WSlxWglK/fn3/MXSyPSFaH374YW+RTrmvYDu9RxeBsE1ui65uq7UiEJ8E3GOzT1DBhDZuJKeffrp/MI1PGuq1CGSOAAYcwnQSyvPVV1+1KlWqpBuaM3N7ir6t3aivd13A6JWyML+HqE8URCxJc8gUyTWpcePGPg8AYjW0MJmQCWihBaNaSrcI6g0VvayPGxftSVmIZBPq4oXBjhKsy4R75h4tXrzYZ7R88cUXjYhTzqKcsir9HUUEwmrxjaJ+q6kiEJcEuEG/8MIL1rZtW+vZs2eyi35cAlGnRSCTBBBxf//73/3kLMSZkjEdBMqcHQRoSrHKt0wIZKQ3KFhdEb+jRo3y3/Xo0SP4KumdcKn43KZ8Ja3w1wdGmQPhGnzHtmmFaWTd0Kyxga82E/EoXCt5oMEXmKyWWLB/+umnoFq9RykBCd8oPXBqtggcK4ElS5b4iRzckG688UY/2/lY69D6IiACqQng3ofbEFENEErOvzT1SnG4hIRWhCQNLYw6ISKbN28euth/PvPMM338fibJpyyki77hhhtSvVK6HyCoudaFHoPZs2dbzZo1U1bpxfecOXOSlgf75XimLMGy0OhTKdfR39FBQMI3Oo6TWikCmSKA1eWNN97wSSpuv/12H7YnUxVqYxEQgWQEEHL4+zIUTpSAeBRIiMggAgLXHB4GvvvuOx/pCZ/eadOm+VBwfMZvlkJ0JyIrYClnuZvMbmnFRv7oo48M/93Ql5swn8rVgSgSbvK8DzWHK8Nzzz1nq1evtu7du/v99e7d2ych4Q8yyn7zzTfe0kwa6v/7v//z0amYj4R1l7BqRIlwk/b8NliCiV6lEuUEwjpVLgsqU1SHLICqKuOKgBvKS3QhlxI7duyY6C7yPspKXAFQZ0Ugmwgw+/yDDz7wEQvc8LiPXpRNuz6uu3GCNtFNbvcREZwk8u8udq5v02uvvZboQib6ZW4Se6JLkpMsUoJLXpXo4u0mbXviiSf6aE+Z6ZCbvJtIRAbaUqZMmUSORVCuuuqqROda4f901uJEF74s0flq+3WJ0BFElyCag4s7nNQu53Oc6MKzBdXoPRsIZFVUhwTaHsnafejQoT4V8iWXXBLJzVTbRCAiCWD5ICsiM5MJun/NNddoYkZEHik1KlYIENuXxBYMm7sQWnbaaacp25c7uFiA8fkNnUwWHHNkCG4ifJ+WL26w3rG8UydW3JTZ2FzoVJ+NjSRZQcEHmFfg2xsspw5yDtCulN8F6+g96wjwW3rsscd8lsSUkxgzs1e5OmSGnrYVgQgmwEWbCSMkjnHxev1Qn2YjR/ABU9NiggATpm699VbvTuSsnTZr1qyY6FdmO0Gq4rREL/USCpVEOuESvUGdKUUvy4kEESp6WUaW2LSELe0i+1ta37GdSnQSkPCNzuOmVovAEQm4IOz29ttv+xBLhOXhhqwiAiKQ9QSqV6/uw3NhXUT8YjVUEQERiAwCEr6RcRzUChEIKwEmmDBphAgO99xzT6rhvrDuTJWJgAikIkA8WiZ3bdiwwYtfQnipiIAIHH8CEr7H/xioBSIQVgJkHXrnnXd8fErClqUMBB/WnakyERCBNAkwTN66dWvvVz9p0iT7+OOPfUKHNFfWQhEQgWwjcMi7O9t2qR2JgAhkFQEmkBCuh5A/d955p7/xZtW+VK8IiMDhCeBP6qKp2IoVK1wJnKAAACwGSURBVHzsWnxFL7vssnR9XQ9fm74VAREIBwEJ33BQVB0iEAEEyGj0xRdf+JiUvXr1svbt25sLHxQBLVMTRCB+CTBxiogqW7Zs8fF98bW/+OKL9duM31NCPT/OBHRXPM4HQLsXgXAQIEUnaTUJuE6g9i5duqSauRyO/agOERCBYydAWmOSW5x88sneDYnUvEx8UzlGAm7Crp1/PjmPj3FDrS4ChwiEXfjyYyZ2KKGUQkuwPPTHzjpkt9m3b1/oqvosAiJwDAT4DSF4yRZ1zjnn+KFUF5D9GGrQqiIgAllNoESJEnb99dcbk97eeustmzhxYqr7ZFa3IWrrdxnYzGWctHPPNfdUb+ZCo6mIQEYJhNXVgdmrLrOJMbnGZV/xL27ACNuff/7ZfvrpJ//Ee/rpp/s0g6QEHDt2rI+hd8EFF/h4eRntiLYTgXgkcODAAZ8SlIkzBMq/9tprFbYsHk8E9TkqCFSqVMnH+CXBxUsuzFlO5wZxokt1nBAVrT+OjfzsM5eDzRnTZs82cw8QKiKQGQJhs/hivZ0yZYotXbrUKlSo4J9mly1b5tvGd4ULFzbyZi9ZssQL4Z07d9rw4cN90Go+T5gwQUM/mTmS2jbuCPC74mHyjTfe8JPYbrrpJnMpNuOOgzosAtFEgBi/tzvrZaldO2z4iy/aAiW4SPvwLVx4aLlLCGL/+59E7yEi+pQJAmETvtu2bbPly5dbnTp1rFOnTj4tKjPLuTlj9W3unmpbtmzpU/8x0/W3337z2VrIKNWmTRs/C93lZU7VFU3OSYVEC0TAEyAr2/PPP2/VqlWzu+66yz9wCo0IiEDkE+B++J96je2kTz6xjx9/1GYvWBD5jc6uFrqRY3OTc50wkC9vdjGPs/2ETfji18uwKzNYEbakRiX3NcKXQkzD4DN/k4OZ9IUs5x13CHwVgzJ//nyfanXIkCGa/RpA0bsI/EWArGwkqChTpowPW8a7igiIQPQQKJqngFWwEjZ63Cx76ZXXbMniRdHT+Kxqaf/+ZiecYM5CZjZnjlnp0lm1J9UbxwTC5uMbCF7cFhDAu3fv9lmjQi22WH4RurwTzxArMYUwTOTORiwHhVmwjRo1MuKShgrm4Hu9i0C8EsA3Hksvv6H777/fatWqFa8o1G8RiF4Ce/dZrgrlbH+t0+3TH2dZXnvR/Z7vtapVq0dvnzLb8po1zb791tzNP7M1aXsRSJdA2IRvwYIF/VArqVIRvVh7SZdKjnJmszLhDSsVUR3wcSKbFIJ25MiR3kWiSpUq3g84aCkWLF5MmENMq4iACDC3Y7Y999xz/vf10EMPWd26dYVFBEQgGgmULW3bq7qH1urNbFepKvbp6CGWO89r9o8H/+7vfdHYpWNu87p1Zs8+a+Ym+7nhYnMhL465Cm0gAsdKIGyuDlhyiVGIlRYLbocOHdwoRWnDbxc3BvKUly1b1i9b50523Bu6du1qxB8tV66ctWvXLs24o1iPVURABMyw9D7yyCPe9YdZ4Q0bNhQWERCBKCWwv2tnm3797baiXGUvfreccJG9NXS8Pf30Mz7TW5R26+iaTQjTV1456NbgtIMbJj667bSWCISBQNgsvrSFoVfSMyJWcV3AossLn1+c+Zs1a+abjEjGBQKrL8O0/M36KiIgAmkT+PXXX+2xxx7zk0MRv/x2VERABKKbAJovgXkwOXJaQtXGtish0d4f2s/Nd9nt3B4esMqVnSiOxYKV14U+tR9/NKtfPxZ7qD5FMIGwWXyDPiJyA19exC1/UxC2LOcViNzA3zf4O6hD7yIgAocIECbwn//8p3cdevzxxyV6D6HRJxGIWgI5vxhgTV59ziqvXenUbw4ngJ0KrtrEtjToZB+MmGhPPvWkLXXhP2OmhLos3nffQV9eid6YObzR1JGwC99o6rzaKgKRTmDatGn2r3/9y4+QPProoz5cYKS3We0TARE4CgJu4naBjWstl7PuumFPS3TWXvfBEmq0sO2NOjuf36n27yeesLVunkxUF6I1ucm4Vru2uWD+B7sSMpE9qvumxkclAQnfqDxsanQ8EPjWzW4m0D3DnS+6QPe1uXGoiIAIxCwB3B4Sczi3vxotbXurK+2jn+bZXXff7ePeR2WnXYIda9rUbNQosx9+MHPRmlRE4HgTkPA93kdA+xeBNAgQ7YRQZS1atDDcG4h6oiICIhBDBFys2r1Fi9gB598bWhC/3u+3Qj3be0oP+3raEpeg5m6b7fz8o664yev21FNmw4YdtPhGXQfU4FgkIOEbi0dVfYpqAp9//rndcccd1rlzZz+hTckpovpwqvEikCaB/ZdfYtNvusdWEtXBhflMWbz4LV3did9r7bslO63XzbfYuHHjUq4WWX+7RFb24YfmZrUfbNe555q7kEVWG9WauCcg4Rv3p4AARAoBYl8/5awjDz/8sN3thjeJ3kAiFxUREIHYI5BYvJhtL1vOdud2iZsO/CUUU3QzIdGF+Spdzfae0cvG7S5jV1xznQ0ZPDjFWhHy5/DhBxNPDBhgLjtVhDRKzRCB1AQkfFMz0RIRyHYCJGkhcsO7777rrbw33XSTj4CS7Q3RDkVABLKFQK4vvrZWb71oVdYsd2GPkrs7hDbAW34LlrDEU66y5SVb2m1332d9+nzqQ4WGrndcPz/zjLnc6ebyqJshfIsUOa7N0c5F4HAEJHwPR0ffiUA2EFi1apW7Z9xpI0aMsP/973921VVXJYUBzIbdaxciIALHg8DylVZ43lzL86fLTEpA38MUb/nNW8AOnHa5LS9/qt3xt3/Ys0//N3Kyml53ndmsWWa4NqiIQIQTkPCN8AOk5sU2AVIQX3vttTZ37lzr3bu3u2/oxhHbR1y9E4G/CLg494kurv2RRG/Ay096S3CW4ZO726Ym3exfz/3P7rj9NhchbEuwSva9425x4omHXBpKlTLLmzf79q89iUAmCEj4ZgKeNhWBzBD48ssvfdruihUr2meffZaU2TAzdWpbERCBKCGw3/nv7nSTwSju47GUhMbn2u5zH7QPv51ul156iTO2OmtrdpTffzfr1Mns738/GK2hcOHs2Kv2IQJhJSDhG1acqkwEjkwAf9433njD+/QSueFZl75T4cqOzE1riEBMEeh+kc2+9wFbX7aii4KQOqrDYft6YK8lVKhvCef/zb5ftMN6XHONffPNN87v9xgV9GF3ksaXzh3L2rY1mzHDrEOHNFbQIhGIfAISvpF/jNTCGCKwbNkye+CBB+ytt97yURvIxlayZMkY6qG6IgIicDQE9tapbSsaNLP1BZzVNJ2oDoetx4nf/UVKW2Kn+21GQlW7/tY77T9PPmU7duw47GZH9SXJJoIyaVLwyey228wFGDc38/bQMn0SgSgjIOEbZQdMzY1eAjOcleQ2d+PAr/c///mP9ejRw7nFyS8ueo+oWi4CGSeQe+T31qh/H6u8aZ1Zzozdipn0liNvIbN2N9jq2ufbv9/4yB5+6CFbsmRxxhv28ccHY+8ifjt2NLvhBnNqOuP1aUsRiDACGfu1RVgn1BwRiGQCm11++tdff91uueUWq1atmr3//vuaxBbJB0xtE4HsIDB+klUcOtCKbtlo5ia6ZbQkJrgYwDldmuNm59ufZ91jLw8Zb1dec60NdGHF9u7de2zVrl9vdu+9Zn/8YXbGGWbnnWc2dapZwYLHVo/WFoEIJuB+LSoiIAJZQeDAgQM2Z84ce/PNN23y5Ml20UUXefFbtGjRrNid6hQBEYgmArlzWWKBfHbgCKHMjqZLRHxIdDPkcpStZQfa32bjJve3O//+iC1eusQu697dypUrfzTVmMucY7Zhw6F1mzd3MYYlEw4B0adYIBDWM3rXrl3+Rr9u3TqrX7++Va1a1UVqORifkFiliIDczjeoSZMmVqhQIRs/frx7sPzDD/c2a9ZMvo6xcEapD54Afnbff/+9vfbaa5YnTx574okn3JyQtkpKofNDBETgIAHS+u4+RovsYdh58cskuWLlLKHNtbZswVj750vv26RJv9idd9xuLVq0PPz1hwlrK1aYe0I3dzM++AoVwYfZt74SgWgiEFbhiw/jkCFDfEaZBQsW2GWXXWZly5Y1UrEOd+kMf/vtN8MKtnHjRjeKcoa9/fbbfugXgVy3bl0J32g6c9TWNAkkupvZ7y7kzxdffGEjR450oS5PtJtvvtlq1aqV5vpaKAIiEKcEWre0Fat22Jb8JdzktvBFY/DxfnPls8QT2tuOwqWt79RhNv/ev9st111tXbp0Sf8+6wxS9uOPcXow1O14IhA24UuIJiy6TZs2df7wHb0f47x587zwZSb7BvfkyMQe3hEFCIISJUrY+eefbw0aNHAZDtNOcRhYjOPpoKiv0Ulgy5Yt/sGP+LyU22+/3QhXpgls0Xk81WoRyEoC+zq0s18TKtqa8WvM/nSW2oy7+aZqJn6/OQ640dZqTW1v6Wo2de4Pds/Tb9qPY36y6669xt1/Wzu3XfntpgKnBXFBIGzCFzeHffv2WWEX0Bp3hvz583s3Bihu377dp2DFvYH1sIph+S1durT169fPW8a6detm9erVS4KOu8Ty5cu9mK5Ro0bScn0QgUgjsHv3bn+e9u3b137++Wc79dRTrWfPnlanTp1Ia6raIwIiECEEco2faHWH/2xlc9SyDfmKu1i+4bP60kU/6e2AE9QF3JyCZp1se7k69tm0ITZlziN27WVd7GJn/eXempAQRsUdIWzVDBE4HIGwCd9czgEe6yyzSBG2+/fv976N7JzvWIYw5sVnnjYffPBBL4hJ1YpgYDiYdSm4QzAhCPeImjVr+mX6TwQijcDixYv9gxsuPjzw3e9iXJ555plWoECBSGuq2iMCIhBJBL7/2aoN7WfFT7nOrLLzqSWTWxYUQp4lOHPygYr1bL/z/507f6w9+W5fGzNukt3Y80o77dTTrYRiiWcBeVUZqQTCJnwRssWLF/dWWuKUMrmHv7Hw4tKQw4VrmTlzpm3dutX/jUhmaBghjPWXCUAI4qAwOY4XfpLbtm0LFutdBCKCAJMyeTDr06ePLV261Ft58WkPHbWIiIaqESIgAhFLgEhkzjab5e3D+su+Egs6y3LTc2xr2Ro2dO73tuDx56zLWROt6yWXWIOGDf1IbZY3RjsQgeNMIGzCF0tt69atbfDgwTbAxQ886aSTvNVr7ty5fuJaixYt7AcXEJv1LrjgAj/hbdiwYbZ69Wr/Y7v00kvTnHF6zHEIjzNQ7T62CfDgNm3aNBs4cKDNmjXLmrtwP7169TKikgSjFbFNQL0TAREICwEMPWGc1HY0bTpo/c1pVqmhHShT3RYsnmYvDBlnQ38Yb13ObmtdL73E6tapa3mUWOdocGqdKCUQNuFL/ytXrmzXuJzhRHHA15eCNZfJPfg9Nm7c2Ft++Y7lXbt29a4R+fLl8+HN/Ab6TwQikAAjFzzE9e/f31t6iVaC4GUiZ3oTMyOwG2qSCIhApBBo3MDWtD7NthUplq0COMn3N3d+S6h9ku0tV9N+XTjZFvX70cb+MtW6nNfRzurQwao7/19GYlVEINYIhFX4AgeXh7Rmi2INw/UhKLg+KJB/QEPvkUpgz549PsXwt99+a+PGjfMPcUzERPBWqFAhUputdomACEQ4gb3nn2Oz8ta0lZPWuqgOzr83m+eYYf31pUgZS2h6ru2s2thGu9i/U9/sY8NH/2gXnN3ezjnnHKtUuZKbixN2qRDhR0fNi2UCOptj+eiqbxkmgF85PukI3l9++cU/tBGaTII3w0i1oQiIQAiB3FNmWPUfxlqpA1VsQ14XeSFkjkvIaln+kbi/vpSobNbqEtuyeaUNXTTFxr7xlX05aKid376dtXcWYObcyAKc5YdDO8gGAhK+2QBZu4geAgheJq2NGTPGJk6c6P3UO3XqZGeffbZPtpIzp/OPUxEBERCBzBIYM9aqDulvJU660qyiS2Kxf19ma8zU9liAE51lN0fp6nagWHnbsmGZjV40waZ/NNCGfz/GLnIuEKecfLLVdWFHCVeqIgLRSkDCN1qPnNodNgKE3tu0aZNNmDDBC14yEBJjGgsvaYaJx4trjooIiIAIhI2AmwuTe/cOl2jCxdqNkJKU9jiX8+0tV9usVBXbtH6Jfbt8uk1+4zNrPGCotT2lpbV3mVebN29hhf6ayxMhzVczROCoCEj4HhUmrRSLBJiESZKUUaNGuXz2k3yEkTJlytgNN9xgrVq18hZeZQ6MxSOvPolABBBwE7xz7NlrOQJXgwhoUtCEg+4PzgUiZ25LLO8S8bgIEJs3LLUfV861yf1+ssGjx9vpzRta+3anW7PmLa18+QqWK7fkRMBP75FNQGdqZB8ftS4LCPz+++/266+/+qQpRGogoyBps4lI0tDFsixVqlQW7FVVioAIiEAIgXp1bE2rk2x7oSLHzb83pDXpfvQiOIdLUOUyv5lzg/hz+8k2bbW7ho6baV/99JrVL1PA2p7Uyk5v08ZfR4l4oyICkUxAwjeSj47aFjYCxN9lshqWXVwacG2oVq2anX/++XaGG7bjs/zWwoZbFYmACByBwP5O59qveavZ8hlbzXY7d4cI96ZKdC4ZiTlyWo6iLgpE4ZK2t0pDW71+qa1ZM88mfP2z9Rs+ylo1rGMtW7W0Vi1a2gmNGvkoOEfAoK9FINsJSPhmO3LtMDsIkPiE7GqkvCYd9rx582zFihU+vjTJVYgpjZW3fPny8t/NjgOifYiACCQjkGPNaiu1ZKEV2lPQ1udgsthf0RWSrRVZfwQ+wAmJCZaY31mqq5xgCRXq2s5t62zmusX265zfbcDET6x26X7WrH5dO6lVc+c2dqJVrFTZ+wNrrkRkHc94bY2Eb7we+RjsNzF3161b5wXu+PHjbfr06bZx40afEbBWrVpGdAZC8mDdJamKigiIgAgcLwIJw761On0GWdlml9pil0LYImiS25GYHEyBfFCoEwnCilf0r8SqzWzjH+tso5sQN9W5QgwbP9PKF//SGtaobO1Od0msmjS1cs4fmLkUKiJwvAhI+B4v8tpvWAhs3rzZW3WJxEAK4UWLFtm+ffusYsWKXuQ2adLEW3dLlCghV4awEFclIiACYSGwZavl37Tecu3dbZaQEJYqj1clByfDOZt1voKWK18NO1Cquu2pdaIt3b7Zlq5bZFPmL7cBk/tYiRzvWsMqpa1J40ZWzxkh6tWrbxglmGehIgLZRUDCN7tIaz+ZIpDoZj4Tdmznzp22ePFiQ+jixsDn9evX+8DqNVyKTXx2q1ev7t0YsCpg2VVkhkyh18YiIAJZQYBoDgfcK/I9HI669whg5wlsCe5frryFbF8+J2iLV7C9+/bYxq1rbaNLjrFw2xobOXiylRw42qqXLGDVq1ayenXrWH0XH7hB/QbeaJE3Xz6XLU4x048avFY8JgISvseESytnF4Hdu3d7kcuktJUrV3prLkIXP12svFwUmT18wgkneJGL2C1XrpzPsEZ6bBUREAERiGgCxYvZzkoVbF9uFzP3r+zBEd3eY2gcrhD7nQh2b04C57ADefK5iBBVLcHFBT5wYJ/t3LHZdjpr8HInhsfMW2zFpo60UjmGWInC+axy2ZLWuEE9a1i/ntWsXcdKly3n52YUKFDAdG0/hoOgVdMlIIWQLhp9kV0E8M1FzG7YsMG/ELqEGVuyZIm35uK6ULBgQcNdAaFLyDEmphUvXtwPkXFBlFU3u46W9iMCIhAOAvuuvswmlm5sS+ftNNvjsrZFeFSHjPb5oD/woa0TXGi0xCKlLUehMpZYtpYl7mthW/bstC07XHSLjctsysrl9sNv4yyfswgXyHHAKhYvbA1qV7XatWtZjRq1rIwzeJRyCYaKFSvuXsUkhg+h1aejJCDhe5SgtFrmCezYscOFvlnjE0WsXr3aW2/5m9fatWtt165d3jWhaNGiVrVqVWvWrJkf9qpUqZL/G6FLrvjcuXNnvjGqQQREQASOI4EcO3dZwR3bLQ/uDk4MxlPBEowgtgSn9vM6v2DcIgq7MGlla9p+ZxHe6IwhtnOz2bb19tv2TTZxzibbP/kny7VrkBXL4eZwFHYjfiWKWvly5a1ChYpuwlx5H6GnfPly/m9GA3WfiKcz6tj6GvZfG9mwsOClHJY44LLUIHwIZ0K8VN7x2WQZwxesrxI9BPC55ZhyDIN3PiNeiayAsMVyi/9t8MKqu337du/CwDFHyGLFReS2a9fOi9xgGSmDmfCg8DfRc06opSIgAkdPIMfAYdbwk8FWtlFnW+oSQ0RTVIej7+WR1zzkF+x0MGHSXLY4y+/cP/I7/+CSlZxCTrRd+51F/M/ttmfXH7Zz905b8+dWO7B9oyXMXGM5xy2yogl/WtGce6xw7pxWrEgR5xpR0Eq7RETl3DyPChXKuSgSpZ0rXHkrW6astxhjQMmRM4e7v7i4xE6LBC+NHB75eMXCGmEVvgxNf/HFF7Zs2TIvZAgfhchFGH333Xc2bNgwL3Ivv/xyb83r16+fjRkzxoq4E7VXr15eAMUC1GjrA4I1eOFWQAxcHl5SvhC1iFeSPwRuCYQLI14uDzD447JNcBHBDxfrbcmSJX34Giy4VapUscqVK/shKiae5XOTGDhHeGkyQ7SdOWqvCIhAhgms32AF1q60PHWiP6pDhhmk2PCQW4SzBv9VEMOWI7cdKFTcjJebPOe08MEHBRcRY9++3bZx/17b5N4T/9xm5vyGXX5ly716k+Xfu8Ly7NtuuQ/ssTzOuJwrR6LlyZXDihVywrh4UStdwhlfihWxks4AU6p0KSvlhHHxosWsUJHClidvPjfCmNe9cjvr8cGRxjzunoXRhntVThfGLVeug8I5aKveo4NA2IQvwmny5MlexN544402cuRIIzVsI5e9hWFsQk1ddNFFtmXLFvv++++9z+bs2bPttttus4kTJxpxVxnSjnfxw0NC8IJpYFkNlgXvgVDlHbHKK63PLEPIBoKWz0wcwzJPhAQEK4KWz7zzNy/WCdblnReF4SMEayBWscpiscXXCmstL6IpMNGM90DQclz1NB0dFwW1UgREIBsI5MptCU44JWDhzOUskLHq5BsmlKliPLgFCbkL2L6/fKO9VEYRJ7oseO4+updXops1uI+X86PGdWLnFrPt7rV7u+XavMPyr3NCefdaS3BRJxKceM6RePA9p9sub55cVrRgfitaIK8VLpjXijjjTOGCBayAm29SoADGmgJex+R3nwu4zyzn3hi44yGQc7uXF8p/fc4Z/O3uh9xLuS/yfWAs4p1lR/o7TEjjtpqwCV+sflgCEUF169b1Ynb58uVe+DL0TUEEM+z9yy+/2JQpU7xPDiGosCIimhFcWH9DCydAdpfevXv7tLaITIRnUFJ+Dv37WNdhW17sA3EaCNrQd5azTlrfs4xXIHoD4RtsH7pN8Dl0neCHFfzIQt/5IYaKW8Qrk8sCsYtbCoKXZaxHQdTyUMOxJJZuaEnJKeXfoevqswiIgAjEOoFEd71s89MoZ5VcY7tmDDNbMtld62MstEM2HETuzukpBEKqHcBY/NctnM8Ulru7r+2znLYtl9MbOQs7Yex8ivfucpMM3ctZh+2As8Lv2GMr3Chmwt49lsgyv45798fJVep8kf1nH5KOv53gdvvI6QRtbudykfsvi3AuL25zOkszVuIclsst5z0QxYHwDb0HBwKY+yrLQ79jGdvwzot1Qz/7PrrlQeE7X1jffUj6++BC52Z9cLlvvFvh0JYHN3MbuH4m+jYwMt+0adO/vojet7AJX8QVhQMUHIRgWfAeHEDesTgGzuccxEAEBignTZpkffv29bP7r7vuumBxtrwTUWDUqFFeWAY7TH6yHFwaLAveWcpn+hK6LFie8j1Yh/dA4PM59O/Qkzr4LniHY/CjCdYL9sE66X0Otj/cu9/4r/8CoYpFmBcPOMGyYL2Uf7M8rWXB+noXAREQgXgm8FvenJa/7QlW1lkZz7BV8Ywi+/ueTN0d+oPQa2Yu9FqCe4WUv7TzwSXu/u4L7+518K+Dnw8m8vjLFYNvDn7p3txDjf98cIG/N7Ktex1wwvmAE9PoJIxTftlf3wXreYOWW+b357c5+JDkv3eNodZg3dDPBxv613d//eFbQP38TZ0pSlAni/3nvzQNAr5Lly4p1o7OP8MmfLH+IcLw82RYHOstE5coWAc5qNu2bfPL+YxlGCsvYNkGyyH+nkHBH5SsW4MGDfLW0GB5drw/+uij9vDDDx886JnYYSA+M1LF0Wx7NOtkZN/pbRP6g0hvHS0XAREQARE4CgIICrdaehbLo6hBq8QIgSPdW4/0/eEwZGbblPUy6hsLJWzCFyCkHhwxYoT37Q18QRcsWGDM0MeF4d133/WimFisLVu2tHHjxtmrr77qowAwES5U+AbWYIbVsQ5nZ6EdoW3Jzn1rXyIgAiIgAiIgAiIgAllDIGzCl+adfPLJVsqFECEuKwkGsAAjWhG93bp1szlz5vhl+PpiIb755pv9pDcmRmHdVREBERABERABERABERCBrCIQVuGLlRbByytlwe3htNNOS7aYWf/t27dPtkx/iIAIiIAIiIAIiIAIiEBWEJB7UVZQVZ0iIAIiIAIiIAIiIAIRR0DCN+IOiRokAiIgAiIgAiIgAiKQFQQkfLOCquoUAREQAREQAREQARGIOAIRL3zDGYoj4uirQSIgAiIgAiIgAiIgAqkIELI1KzRgWCe3pWp1GBbQ8bFjx/o0gKTRzY4C6D17XG7vPHlSJaLIjv1Hwz4IqE2wbSY0Znc84WjgAxPiVcMpSOoSDe3OzjbCBkZEf9E5lDb54BwKwjumvVZ8LxWjIx9/rtUUzqOsEBJHbkFkrxHcz8gnID5pHyt+Z7DJznNo586dPiNs2i3K+FKXaCSN1B0Zry/sW65du9anN87OCz/pl8ka17VrVx+KLcIRhZ35kSokS9yyZcvs559/ts6dO7u85QV0sUgBDUbz58+3hQsX2plnnukfolKsEtd/wmfp0qU2bdo0H9mFJDf6nSU/JWA0Y8YMW7JkiZ133nn+ASr5GvqLB6bp06fbihUr7IILLsj2ZEfRcAT4Xf3yyy+2ceNGO//888UojYNGttaZM2fa5ZdfLj5p8OFaNGHCBG8QbNOmTbYx4oGkaNGi1qpVq7Be/yLe4lu2bFl/0U/jWGTZIrLO8SM499xzLVYylYQbFjdjLqTckLHYqaQmQLg+BB2MZNFMzWfx4sV+1AA+jK6opCZQuHBh//B9zjnnpP5SSzwBYsIjXBQaM/0TAuGycuVKMUoHEfkHsIrrHEoHkFvMAxSj7rHAKOJ9fNM/DFn3DT8ABHcwPJR1e4remhFywcUienuRtS1nlIKnVVJ4q6QmwDlUvHhx8UmNJmkJDwQk+NG1KAlJqg8Bo1RfaEESAUbluBappE2AazX3M5X0CWAE5DyKhRLxrg7HAzI3mVWrVlmFChVkzUznAOzatcs2b97sGaWzStwvZuQATrqgpn0qwAa3IizjsoinzUjnUNpcQpfCCF/A0qVLhy7W5xAC27Zt89Y6XYtCoIR8DK5FGLxU0iawZcsWf52OhQcojVGncYwZuq9SpYr/hgvG6tWrrVq1ahqODWHF0x+cFi1a5MUdQ7IVK1YMqx9OyO6i8iMTJTZs2GD4qePyUL58eZ1DIUeScwhLy/Lly43fGQ+aWIBVDhFgki0uRQi7cuXK6fw5hMb7GXJt5oYswRICJuTjn3/+6Y04CDsECxOUmGyrcogAw/f4iGPwgg/nkhgd4hN84n7PvYzrdrS7puV81JWgY3pPTWDw4MH29NNPe78WxJ3KIQJYfEeMGOEnHzLBpHLlykZqapWDBBAsAwcO9BNL8BnnxoO4UzlEYNOmTTZ06FD76KOPrGTJkla7du1DX8b5p+3bt1u/fv1s9OjRNm/ePP/bQvyqHCSAUAnOHQRe8+bNhSYFAR4MuIcxuW3OnDn+4YnfmcohAow68TvjGj1r1ixvwNED+CE+fOKBgPPo7bfftpYtW3r3q+RrRNdf8vE9zPFi8g1PgvhocuBVkhNA5Hbr1s2uueYab/397bffkq8Q53/xoHTJJZfYfffd5629U6ZM8bNi4xxLsu7DqGPHjla/fn1vwVNkh0N4uPYgXK6++mqrWrWqj/CAwFM5SACrXNu2bf0Li7hKagIIuO7du/trENdrxJ1+Y8k54UN/ww03WI8ePWzr1q2m+1hyPvz1+++/ewMXE0kZPYj2IlcHdwQZKuOpLyjMgM2XL58P30EYDS4W8T70gWUOCxSFCyfDHlxI16xZY8OHD/czhjt16hQgjLt3Lpi8KPDhfMHCi/8q5xbs4tkVBCb8znBpCGXEOcTQIq4gKocIwIsRA27K8MH16tdffzX8Wbk2qZhxncZ9iN9ZLNyMs+KY8rvixfWbhyZYyZ8+OWnOI0YvP/30U38ecZ1WOUSA84bQpSeeeKK/BsXC+SPh644vwxsMBQVWXXwzuVhMnDjREHNMdEP8cpGNhYN+6JQ+uk/E0sNaSUxRbsj8zZMfYU24SGB1wSq+bt26o6swBteaPXu2f1DiHIIR5xDxDuvWrWvffPONX3bqqafG7QMU5wznz6RJk/xviL/5jZ199tlJ/vQxeFpkqksw4noTvDiv4vH6cziIMOGlkj4BHrqDaxDD1CqpCWAZ79Chg3333Xe2fv16f07pt3aQEzqIF9fqBQsWeIs497Vo5iPh645tixYtrEGDBkm/Bg4obg4IOQ40Vk3+5kYUj5ZfnohPOeWUZD50MGJiEjwYpp46daq3+iZBjLMPzZo18yI36DZ8mACANZxEFl26dPHW3+D7eHvnPMFi0KhRo6Suw4gHKB6amMTFiwcHRhPivcAGazhWciaUEIMVVkwsUTlEAD/f4Nzhs86dQ2z4hCV85MiRXqzglobFVyU5ASya3OO4No0bN867F8XrvT45mYN/YcSpWbOm9xHH9QpDYLTz0R3GHVti06WMT8dNBzHDAV7ikjVg+Y1H0Rv8ELjp8got3IyxJHBxZTj/wgsvDP06rj4jSFKKEi4QTL5haJq02wzzn3TSSf4iG1dw/upsWr8zrFFM3mJyJOcTEyR5EEX4xXsJJot+9dVX/pw566yzUp1j8cwIofvjjz/amDFjfNQLPp9++ulRP+M8nMeU7IhMsMWXfvz48f7BsmHDhnF7DUrJltECrtPffvutf4DCV7xx48Zxfa9Pyah169bGC0s4GogR3mjXQorjm/Iop/E3bg7MNk8pbNJYNa4WIXZxE+GJGV9WLL+yuBw6BeCDoMOiiUWhUqVKVqtWLYm6Q4j8uUPEAiwJMGIIjYlcEr4HIRHqjYklPIjXqVNH16CQc4fRATK2MQmQwoMC54+uQYcgEU4R3/DAQlejRg1/HdLv6yAjhC+jKjBi5CC4Rke7sDt0BoTvE3wwAhKZCDe1aC4SvtF89NR2ERABERABERABERCBoyagcGZHjUorioAIiIAIiIAIiIAIRDMBCd//b++MVVqJoig6jW2aGCz8gRSCkDpNSk2RSrBVSOqAHyH5BO20kbRB7AJCQGwsLLRLivyBoIXdYx24vnnyEIsEdO66kBcZZ+7MXSOPzeHcvX/z2/PZJSABCUhAAhKQgAS+TUDh+21UnigBCUjgewTYSERP3FcDt5jJZBKpUWx+XIcXLT2M7FFg0w6WRGzkYSyXy9ilzYZL+tAdEpCABHIhoPDN5U27TglIYKUEvvKPLYtYzmNz0eeBVSKOFojR6XQaVkqck87/PD9z/O9Yed50bTqGMf/NzU3cfz6fF+PxOBxY2OmPRSMbU5N3abrGbwlIQAJVJqCdWZXfrmuTgATWQoAkrOvr6zC9J5QD14VyQAmBOK1WKzxUca3A2QPXk16v9+FYwbFmsxmx31R+qcwSeoK1Em4F9Xo9LAJxdqAijEhlN3W3242AFKwEsRjC3QDzfXZbk7DEzmuS3rAX5Nkw58dSb29vrxiNRsXZ2Vm4aBDRisUc3q63t7fFwcHBWlg5qQQkIIGfRMCK7096Gz6LBCTwKwgkO5/z8/NoFUBcYseWBgKUVgcEMNZR7XY7PGcJo0iD47Q70IJAZRYrLmyUGo1GCOnn5+dITKQyS3WYkB1aE+7v70PgYlWFLzQBKVRzCUvBXhC/7dlsFj8TLIMVI/PyjJ1Op7i8vAyBTRwyISubm5th55Sey28JSEACVSbw93/qKq/StUlAAhJYIQEEY6rOIhx3dnY+KrncBlFLawIilCAcPvyM0C0P/IsRsohXqsakRSJa8YAmoAGPWirDJCchnre2tiLJjR5djpGoiLDl3MViUby9vUWiIiIaYYugJryA56ENIlWiuV8arIVqskMCEpBADgQUvjm8ZdcoAQmslAAikkot7QxUXknIKo/U00ullUCF1JtLW0IaHCMlajAYRDISVWLEKwl2tC5sb2+HIOU85qCinOah4sx9aXVALCNsEbiEXBCPfXh4GIEOiF9ENIM+Yja5nZycRKvD09NTHEdY0wrhkIAEJJADAYVvDm/ZNUpAAislgECl6jocDqO39uHh4R8XByqziN5arRb9uAhTWg3IvU+DJEiO0ctL1O7GxkZUd7n24uIiqsNUgakUMw9zIHg5n35iqrm0WtADjMDd398vXl5eitPT0ziOMCZqlDYJWiTu7u4ieh2xjbCm0sz5VKF3d3fTY/ktAQlIoNIETG6r9Ot1cRKQwDoIvL+/RzUWQUp7AQOBijhlIDoRtbg7IGj5vL6+RuQwPzOYgxYFBDCV3NSmwPF0Hb9jTirIbESjJYFzuY6KM60Qj4+PxfHxcVSPEbJUdakQI5qZk81s/X4/rqMqzP25Bx9+f3V1VRwdHcXzxoP5jwQkIIEKE1D4VvjlujQJSKCaBGhfoIJLmwPOEFRsy9Xk8qppnUCEI5w/DwQ27RK4QDgkIAEJ5EBA4ZvDW3aNEpCABCQgAQlIQAKFPb7+EUhAAhKQgAQkIAEJZEFA4ZvFa3aREpCABCQgAQlIQAIKX/8GJCABCUhAAhKQgASyIKDwzeI1u0gJSEACEpCABCQggT9KEdgILaHEEAAAAABJRU5ErkJggg==" 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" 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "## Hypothesis Testing\n", "\n", "In lecture this week I mentioned that there are two ways to frame the paradigm of hypothesis\n", "testing: one (which I did in lecture) emphasizes the notion of a \"p-value,\" which is the probability\n", "of an event happening which as as unusual, or more unusual, than the result of the experiment which\n", "you did to test your hypothesis. This gives you a sense for how unusual your outcome is, independent\n", "of your level of significance. \n", "\n", "It is sometimes the most appropriate method, for reasons that we shall explore in Problem 7 below. \n", "\n", "However, the second way of framing the problem is also useful, so I would like to present it here in\n", "case this makes more sense to you. It is another tool for your toolbox of statistical techniques. \n", "Instead of emphasizing the p-value, we will emphasize the level\n", "of significance:\n", "\n", "> Recall that the Level of Significance (LOS) $\\alpha$ of a test is the probability,\n", "> if you reject the hypothesis, that you will be wrong. This could happen, because,\n", "> although the hypothesis is correct, there is some probability that the experimental\n", "> result, due to the random nature of the sampling process, ends up with an extreme value. \n", "\n", "> For example, your hypothesis may be that a coin is fair (has a probability of heads of 1/2),\n", "> so you perform a test by flipping the coin 10 times. You may decide, upon observing 10 heads\n", "> in a row, that the coin is NOT fair and you should reject your hypothesis. However, that outcome\n", "> has a probability of ${1\\over 2^{10}} = 0.00098$ and COULD happen. If the coin is in fact fair,\n", "> you would be wrong to reject it, but you have no way of knowing for certain. All you can do is\n", "> state how sure you want to be in your decision, or, alternately, how probable it is that you\n", "> will be wrong if you reject. \n", "\n", "> Note carefully in this example that if the result of your experiment is to observe 5 heads out of 10\n", "> flips, this does NOT give you much assurance that your hypothesis is right, because the probability\n", "> of heads for a coin is a statement about what would happen in an *infinite* number of flips. So one\n", "> run of 10 flips is not much evidence. Thus, we can Reject our hypothesis, or Fail to Reject (just\n", "> leave the hypothesis as it is, as a unproven hypothesis). \n", "\n", "#### Critical Regions\n", "\n", "For any distribution, we can define the three following critical regions of the PDF which\n", "indicate the extremes of the distribution whose area is equal to the LOS. When you do an experiment to test a hypothesis, then if your result ends up in one of these regions, you should **reject** the hypothesis; of course, you might be wrong because of the random nature of the experiment, but you will only be wrong LOS percent of the time!\n", "\n", "\n", "\n", "**Two-sided Critical Region:** The probability/area of the LOS is distributed\n", " equally at both extremes of the distribution (here, we assume LOS = 5%):\n", " \n", "![Screen%20Shot%202020-03-28%20at%2012.35.40%20PM.png](attachment:Screen%20Shot%202020-03-28%20at%2012.35.40%20PM.png) \n", " \n", "**One-sided (Left) Critical Region:** The probability/area of the LOS is distributed\n", " entirely at the leftmost extreme of the distribution (here, we assume LOS = 10%):\n", " \n", "![Screen%20Shot%202020-03-28%20at%2012.55.18%20PM.png](attachment:Screen%20Shot%202020-03-28%20at%2012.55.18%20PM.png)\n", "\n", "**One-sided (Right) Critical Region:** The probability/area of the LOS is distributed\n", " entirely at the rightmost extreme of the distribution (here, we assume LOS = 5%):\n", " \n", "![Screen%20Shot%202020-03-28%20at%2012.35.26%20PM.png](attachment:Screen%20Shot%202020-03-28%20at%2012.35.26%20PM.png)\n", "\n", "Which one to use depends on the experiment, and what you are trying to find out.\n", "We will think about this for individual problems below and define which one to use.\n", "\n", "### How to use critical regions in your hypothesis tests\n", "\n", "The procedure is then as follows:\n", "\n", "1. State your hypothesis (in the form $\\mu = k$ for some value $k$).\n", "2. Figure out which of the three types of critical region is appropriate.\n", "3. Give your LOS.\n", "4. Calculate where the boundaries of the critical region are, given the distribution\n", " of the results of the experiment.\n", "5. Perform the experiment, and if the result ends up in a critical region, **Reject** the hypothesis otherwise **Fail to Reject** the hypothesis. \n", "\n", "Hint on the calculations: In step 4, for a two-sided test, use the `interval` function from the `norm` library; for a one-sided left, use `ppf` and for a one-sided right, use `isf`. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Five (Hypothesis Testing)\n", "\n", "Suppose a random number generator for a Uniform Distribution in `[0..1)` is being tested.\n", "We know what the theoretical mean and standard deviation are supposed to be (because we know how to find the details by looking up the Uniform Distribution in Wikipedia). \n", "\n", "We generate 100 random values and find the mean to be 0.4365. Since the mean value could be too low or too high, this is a two-sided test. \n", "\n", "(A) Test this result with 5% LOS, stating whether the result is Reject or Fail to Reject. \n", "Show all work (i.e., give the bound calculated in step 4). \n", "\n", "(B) Repeat the test with 1% LOS, stating whether the result is Reject or Fail to Reject. Again, show all work. \n", "\n", "Hint: If you write this in Python code, you can just cut and paste your solution from (A), changing one number, to get the solution to (B). " ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solution (A)\n" ] } ], "source": [ "print(\"Solution (A)\")\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solution (B)\n" ] } ], "source": [ "print(\"Solution (B)\")\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Six (Hypothesis Testing)\n", "\n", "Suppose in its advertizing, Apple claims that the pens last an average of 1600 hours. We wish to test this claim, and so we set\n", "\n", "$$H_0:\\,\\mu = 1600 \\text{ hours}$$ \n", "\n", "and a level of significance \n", "\n", "$$\\alpha = 0.01.$$ \n", "\n", " We do an experiment where 200 Apple Pens are tested and the mean of the lifetimes is found to be 1575 hours with a sample standard deviation of 120 hours. Since this is a large sample (>30) we may use the sample standard deviation in place of the population standard deviation.\n", "\n", "I really want to know is whether Apple is exaggerating, and the Pens actually have a lifetime much lower\n", "than hypothesized. Therefore we use a **one-sided (left)** critical region: if\n", "the pens perform really poorly, we will reject our hypothesis, but if they\n", "perform much better than expected, we will be satisfied and NOT reject. \n", "\n", "\n", "(A) Perform the test as just stated. Show all work, including the boundary of the critical region. \n", "\n", "(B) Repeat the experiment with all parameters the same except make the sample size n = 100. Show all work. \n", "\n" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solution (A)\n" ] } ], "source": [ "print(\"Solution (A)\")\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solution (B)\n" ] } ], "source": [ "print(\"Solution (B)\")\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Seven (Hypothesis Testing)\n", "\n", "Suppose I want to test if Richard claims to have Extrasensory Perception (ESP), and \n", "that if I draw a card drawn randomly and with replacement from\n", "an ordinary deck of cards, he can guess the suit without seeing the card.\n", "\n", "I am sceptical and propose to test his claim. I formulate the hypothesis that\n", "when he tells me the suit, he is just guessing and the probability of his getting\n", "it right is 25%. \n", "\n", "Therefore, I perform 100 trials where I shuffle the deck, draw a card, ask him to guess the suit, and then replace the card. \n", "\n", "I decide that since ESP is about guessing the card's suit correctly, I will make this a one-sided (right) test with LOS = 0.05. \n", "\n", "We perform the test and Richard identifies 32 of the cards correctly. \n", "\n", "Now at this point, I realize that if I use the normal distribution, it will be an estimate, and I am not sure how well it will work, because B(100,0.25) is not symmetric. \n", "So I decide for maximum precision I'll use the binomial directly, but how to calculate the critical region and an LOS that goes along with a *discrete* distribution (think about how to calculate the top 1% of B(3,1/2) for example!)? \n", "\n", "So in this case, the \"p-value\" method shown in lecture is best: I'll calculate $p = P(X \\ge 32)$ and see if it is less than my LOS $\\alpha$ (which would mean it has to be in the critical region). \n", "\n", "(A) Perform the test as specified. Reject if $p = P(X \\ge 32) \\le \\alpha$ and Fail to Reject otherwise. \n", "\n", "(B) What is the smallest number of cards Richard would have to identify to\n", "make me reject my hypothesis with $\\alpha = 1 \\%$?\n", "\n", "Hint: use `binom.cdf`. " ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Solution (A)\n", "\n" ] } ], "source": [ "print('\\nSolution (A)\\n')\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Solution (B)\n", "\n" ] } ], "source": [ "print('\\nSolution (B)\\n')\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Eight (Hypothesis Testing on Real Data)\n", "\n", "We will now use the data frame downloaded in Problem 4,\n", "but extract the height data and perform a hypothesis test on it. \n", "\n", "\n", "### Part A\n", "\n", "First we will read in the biometric data on heights and weights from \n", "\n", "> https://cs-web.bu.edu/fac/snyder/cs237/Data/biometricdata.csv\n", "\n", "extract the heights into a Python list, find the ground truth about the mean and standard deviation,\n", "then perform a hypothesis test. \n", "\n", "For this first cell, I just want you to copy the code from the first cell in your solution to \n", "Problem 4, Part A, to verify that everything is working properly. The only change is to use heights\n", "instead of weights. Change the variable holding the weights from W to H!\n" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "# Use data frame from Probblem 4 Part A\n", "\n", "# Convert column of all Heights into a Python list\n", "\n", "H = [ 0 ] # just to get it to compile, your code here\n", "\n", "population_mean = mean(H)\n", "population_std = std(H)\n", "\n", "# print it out, should get 67.9931 1.9016\n", "\n", "\n", "\n", "# Randomly sample weight of N individuals return mean and *sample* standard deviation as a pair\n", "# Use choice from numpy.random\n", "# Ok to just do it with replace=True\n", "\n", "def get_sample_parameters(P,N):\n", " # just to get it to compile, your code here\n", " return (0,0)\n", "\n", "# test it!\n", "\n", "seed(0)\n", "\n", "# print them out, should get 67.6173 2.457\n", "\n", "(x_bar_30,sigma_sample_30) = get_sample_parameters(H,30)\n", "\n", "\n", "seed(0)\n", "\n", "# print them out, should get 67.9344 1.9716\n", "\n", "(x_bar_100,sigma_sample_100) = get_sample_parameters(H,100)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part B\n", "\n", "Now we will perform a two-sided hypothesis test using a sample size of $N=30$ and a level of significance of $\\alpha = 10\\%$. Our *null hypothesis* is:\n", "\n", "> $H_0\\ =\\ \\mu = 65$\n", "\n", "Perform a hypothesis test by selecting **one** sample and reporting your result (Reject or Fail to Reject) and explain your reasoning (the boundaries of the critical region, and where the sample mean falls, inside or outside the critical region). \n", "\n", "Remember that the normal distribution implied by the hypothesis has a mean $\\mu$ specified by the null hypothesis\n", "and a standard deviation derived from the sample (using the sample standard deviation). " ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [], "source": [ "alpha = 0.1\n", "mu = 65\n", "N = 30\n", "\n", "seed(0) # try without the seed to see if it varies, then submit with the seed of 0\n", "\n", "(x_bar,sigma_sample) = get_sample_parameters(H,N)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part C\n", "\n", "Repeat the hypothesis test with $N=30$, LOS $\\alpha=0.05$ and null hypothesis:\n", "\n", "> $H_0\\ =\\ \\mu = 64$\n", "\n", "Again, show the result and explain by showing the sample mean and the bounds of the critical regions. " ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "alpha = 0.05\n", "mu = 64\n", "N = 30\n", "\n", "seed(1) # try without the seed to see if it varies, then submit with the seed of 1\n", "\n", "(x_bar,sigma_sample) = get_sample_parameters(H,N)\n", "\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 2 }