Assignment 4 Answers - MAT2378B Assignment 4 Due date 16 November 2009 Total number of points 30 Q 1(6.39 In a natural population of mice near Ann

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Unformatted text preview: MAT2378B: Assignment 4 Due date: 16 November 2009 Total number of points: 30 Q 1. (6.39) In a natural population of mice near Ann Arbor, Michigan, the coats of some individuals are white-spotted on the belly. In a sample of 580 mice from the population, 28 individuals were found to have white-spotted nellies. Construct 95% confidence interval for the population proportion of this trait. Solution to Q1: ˆ p = 28 / 580 = 0 . 048, estimated standard error= radicalbig . 048 ∗ (1 − . 048) / 580 = 0 . 0088, so that the 95% confi- dence interval is . 048 ± 1 . 96 ∗ . 0088 . (Remark: above, the formula from lecture (see last page of Notes for Chapter 6) is used. There is a little bit different formula for SE in the book: see Section 6.6 “Confidence Interval For a Population Proportion”. Both solutions will be accepted) Marking scheme for Q1: 2 points (1 point for the appropriate formula, 1 for the correct final answer). Q 2. Nine measurements of ozone concentration are obtained during a year: 3.5 5.1 6.6 6.0 4.2 4.4 5.3 5.6 4.4 Assuming the measurements come from a normal population, provide two 95% confidence intervals for the population mean μ : (a) one assuming that the population variance σ 2 = 1 . 21; (b) another relaxing this assumption . (c) For the situation in part (b), test H : μ = 5 . 74 against H A : μ negationslash = 5 . 74 taking α = 0 . 05. (You have to use confidence intervals to answer this here). Solution to Q2: First, α = 1 − . 95. Second, the sample mean is ¯ y = 5 . 01 and the sample standard deviation is s = 0 . 9765. (a) Assuming that the population variance is 1.21: 5 . 01 ± (1 . 96 × √ 1 . 21 / √ 9) ⇒ 5 . 01 ± . 72 or (4 . 29 , 5 . 73) ....
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This note was uploaded on 12/22/2011 for the course STATISTICS STAT 3502 taught by Professor Alyaothman during the Spring '09 term at University of Ottawa.

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Assignment 4 Answers - MAT2378B Assignment 4 Due date 16 November 2009 Total number of points 30 Q 1(6.39 In a natural population of mice near Ann

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