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Stat 145: Exam 4 Review Answers 1. (a) The sample proportion is: ˆ p = 459 850 = 0 . 54 (b) A 95% conﬁdence interval for p is: 0 . 54 ± 1 . 96 r 0 . 54(1 - 0 . 54) 850 = 0 . 54 ± 0 . 0335 = (0 . 5065 , 0 . 5735) (c) The sample size should be: n = ± 1 . 96 0 . 03 ² 2 (0 . 54)(1 - 0 . 54) = 1060 . 2816 Rounding up to the next higher whole number, use a sample size of n = 1061. 2. (a) The sample mean is: ¯ x = 58 + 47 + 57 + 55 4 = 54 . 25 and the sample standard deviation is: s = r (58 - 54 . 25) 2 + (47 - 54 . 25) 2 + (57 - 54 . 25) 2 + (55 - 54 . 25) 2 4 - 1 = r 74 . 75 3 = 4 . 99 (b) The hypotheses are: H 0 : μ = 51 H A : μ > 51 The value of the test statistic is: t = 54 . 25 - 51 4 . 99 / 4 . = 1 . 30

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There are 4 - 1 = 3 degrees of freedom, so the P -value is: P = P ( T 1 . 30) between . 10 and . 15 We fail to reject the null hypothesis and conclude that the current mean retail price for bananas is not greater than 51 cents per pound. 3. (a) The stemplot appears below.
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