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MA 220
E. Lee
Exercise 2
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Show all your work to get credit. Box your answer.
- Independent random samples were selected from populations 1 and 2. The sample sizes, means, and variances are as follows:
population 1 population 2 Sample size 80 80 Sample mean 11.6 9. Sample variances 27.9 38.
(a) Find a 95% confidence interval (in two decimal places) for estimating the difference in the population means (μ 1 − μ 2 ).
(b) Based on the confidence interval in part a, can you conclude that there is a difference in the means for two populations? Explain why or why not.
MA 220
E. Lee
Exercise 2
(c) If your research objective is to show that μ 1 is larger than μ 2 , state the alternative and the null hypotheses that you would choose for a statistical test.
(d) Is the test in part (c) a one- or a two-tailed test?
(e) Calculate the test statistic that you would use for the test in part (c).
(f) Critical value approach: Find the rejection region when α = .01. Do the data provide sufficient evidence to support your claim?
(g) p-value approach: Calculate the p−value and interpret the result at the 1% signifi- cance level.
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