CEE3770_Sum09_HW4

# CEE3770_Sum09_HW4 - α = 0 05 ﬁnd the range of X for...

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CEE 3770 - Summer 2009 Homework 4 (due on 06/25) 1. Of 50 arrows shot at a target, 35 were hits. Determine 80% conﬁdence limits for the proba- bility of a hit. Hint: Use an approximation method. 2. A Gallup Poll estimated the support among Americans for “right to die” laws. For the survey, 1528 adults were asked whether they favor voluntary withholding of life-support systems from the terminally ill. The results: 1238 Said yes. (a) Find a 99% conﬁdence interval for the percentage of all adult Americans who are in favor of “right to die” laws. (b) If the margin error is to be smaller than 0.01, what sample size is needed to achieve that requirement? Assume b p = 0 . 8. 3. We wish to test the hypothesis that the mean IQ of the students in a school system is 100. Suppose that the IQ of students is normal distributed with σ = 15. Using a sample of 25 students, the sample mean X is computed. (a) For a two-sided testing with
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Unformatted text preview: α = 0 . 05, ﬁnd the range of X for which we would accept the hypothesis. (b) If X is 105 and α = 0 . 05, would you accept the null hypothesis ( H : μ = 100)? 4. A random sample of size n = 50 from a population produced the mean X = 3 . 1 and sample standard deviation s = 0 . 5. Suppose that your objective is to show that population mean exceeds 3. (a) State the hypotheses H and H 1 . (b) Perform a test at level α = 0 . 05. (c) Explain why can you use normal distribution tools even when you know that X is non-normal? 5. . Little John had revealed the results of a secret shooting match between Robin Hood and the Sheriﬀ of Nottingham. Robin Sheriﬀ Number of shoots n 1 = 16 n 2 = 20 Average number of points X 1 = 7 . 5 X 2 = 6 . 9 Sample standard deviation σ 1 = 2 . 9 σ 1 = 3 . 1 Using the data above, try to prove that Robin is better archer. Use α = 0 . 05. 1...
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