HW3_SolutionSet - Homework#3 Solution Set Problem 1...

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- 1 - Homework #3 Solution Set Problem 1 Solution: (a) P( X ≤ 70) = P( z ≤ – 0.5) = 0.3085 (from the z -Table) (b) z = 1.645 cuts off an area of 0.05 in the upper tail of the standard normal distribution. Solving 10 75 645 . 1 x for x gives 91.45 ≈ 91 hours. (c) P(70 ≤ ≤ 80) = ) 2 2 ( 16 10 75 80 16 10 75 70 z P z P = 0.9772 0.0228 = 0.9544 (d) z = 1.645 cuts off an area of 0.05 in the lower tail of the standard normal distribution. Solving the equation 16 10 75 645 . 1 L for L we get L = 70.89 ≈ 71 hours. Problem 2 Solution: (a) To test whether the mean difference (after minus before) is positive, we use the following test: 0 : 0 : 0 a H H After calculating the differences (after score before score), we get: n = 40 x = 12.80 s = 10.8017 0 = 0 df = 39 The test statistic is 49 . 7 7079 . 1 80 . 12 40 8017 . 10 0 80 . 12 0 n s x t Using t -Table, P -value < 0.0005; using Excel, P -value = 0.0000000023. Given the extremely low P -value, there is no doubt that the mean score after is greater than the mean score before at all three levels of significance. In fact, the sample mean difference is 12.80.
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- 2 - (b) With a sample size this large, the assumption of normality is not crucial, but the distribution of the population of differences shouldn't be too far from symmetric and bell-shaped. (c) Type I claiming H a when it is not true. That is, claiming that the mean score after is greater
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