Course Supplement Stats 255 – Statistics for Life Sciences I maintained by Dr. Laura Cowen Department of Mathematics and Statistics University of Victoria c© University of Victoria, 2020 All rights...

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Course Supplement Stats 255 – Statistics for Life Sciences I maintained by Dr. Laura Cowen Department of Mathematics and Statistics University of Victoria c© University of Victoria, 2020 All rights reserved. This document may not be reproduced in whole or in part, by photocopying or other means, without the permission of the Department of Mathematics and Statistics at the University of Victoria. Contents 1 Large Sample Confidence Intervals for µ 2 2 P-Values 5 3 Large Sample Inferences on µ1 − µ2 8 4 Formula List 11 5 Formula Review 12 6 First Block Sample Test 17 7 Second Block Sample Test 21 8 Third Block Sample Test 25 9 Sample Final Examination 1 29 10 Sample Final Examination 2 41 11 Sample Final Examination 3 53 12 Exercises 64 13 R Assignments 68 13.1 Introduction to R Assignment 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 13.2 R Assignment 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 13.3 Introduction to R Assignment 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 13.4 R Assignment 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 13.5 Introduction to R Assignment 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 13.6 R Assignment 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 14 Extra Problems 81 14.1 Set 2 Measures of location and variability . . . . . . . . . . . . . . . . . . . . . . 81 14.2 Set 3 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 14.3 Set 4 Probability Axioms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 14.4 Set 5 Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 14.5 Set 6 Mutually exclusive and independence . . . . . . . . . . . . . . . . . . . . . 85 i 14.6 Set 7 Multiplication rule and Bayes theorem . . . . . . . . . . . . . . . . . . . . . 87 14.7 Set 8 Probability density functions . . . . . . . . . . . . . . . . . . . . . . . . . . 88 14.8 Set 9 and 10 Expectation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 14.9 Set 11 Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 14.10 Set 12 Poisson distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 14.11 Set 13 Continuous variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 14.12 Set 14 Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 14.13 Set 15 Sampling, expectation and variance . . . . . . . . . . . . . . . . . . . . . . 96 14.14 Set 16 Expectation and Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 14.15 Set 17 Properties of the sample mean . . . . . . . . . . . . . . . . . . . . . . . . 97 14.16 Set 18 Confidence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 14.17 Set 19 and 20 Hypothesis testing of a population mean . . . . . . . . . . . . . . . 100 14.18 Set 21 Confidence intervals and power . . . . . . . . . . . . . . . . . . . . . . . . 102 14.19 Set 22 Confidence intervals for population proportions . . . . . . . . . . . . . . . 103 14.20 Set 23 Sample size and hypothesis test of a population proportion . . . . . . . . . 104 14.21 Set 24 Testing two proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 14.22 Set 25 and 26 Comparing 2 population means . . . . . . . . . . . . . . . . . . . . 107 14.23 Set 27 Paired Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 15 Solutions to Extra Problems 112 15.1 Set 2 Measures of location and variability . . . . . . . . . . . . .