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Quiz3 - STA3032 Section 7347 Quiz 3 Solution 1-2 In sample...

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STA3032 Section 7347 Quiz 3 Solution 1-2 In sample of 80 tennis balls, the average weight was 59 . 32 g and standard deviation was 4 . 72 g . ¯ x = 59 . 32 s = 4 . 72 n = 80 1. What is a 90% confidence interval for the mean weight of tennis ball? ( 3 points ) (a) (58 . 45 , 60 . 19): with z α/ 2 = z 0 . 1 / 2 = z 0 . 05 = 1 . 645, ¯ x ± z α/ 2 s n = 59 . 32 ± 1 . 645 4 . 72 80 = (58 . 45 , 60 . 19) . 2. How many tennis balls must be sampled so that a 95% confidence interval specifies the mean to within ± 0 . 70 g ? ( 2 points ) (b) 175 z α/ 2 s n = 0 . 7 1 . 96 4 . 72 n = 0 . 7 n = 174 . 6627 175 3. Suppose that we conducted a survey of students and asked them how many hours they spent studying for one course per week. We then found the 95% confidence interval for the true mean number of hours studied per week for one course to be (2 . 3 , 5 . 4). Which of the following statements are true? ( 2 points ) (a) We are 95% confident that the true average number of hours stu- dents spend studying for one course in one week is between 2 . 3 and 5 . 4 hours. (d) The probability that the true mean μ is in the 95% confidence interval is 0 . 95 . 1

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4-5 With μ 1 and μ 2 denoting true average zinc concentrations for bottom and surface water, respectively, μ D = μ 1 - μ 2
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