4. Suppose you wish to test the claim that ud , the mean value of the difference

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4. Suppose you wish to test the claim that ud , the mean value of the difference d for a population of paired data, is greater than 0.  Given a sample of n = 15 and a significance level of ? = 0.01, what criterion would be used for rejecting the null hypothesis? Answer A. Reject the null hypothesis if test statistic is > 2.624. B.   Reject the null hypothesis if test statistic is < 2.624. C.   Reject the null hypothesis if test statistic is > 2.977 or < -2.977. D.   Reject the null hypothesis if test statistic is > 2.602.

5. State the decision rule you would use to test the null hypothesis in the following where H0: ?21 =  ?22   and confidence level is 90%:   Fifteen observations from population #1 and twenty from population #2 result in these sample statistics:  x?1 = 17.45  x?2 = 10.94  S1 = 6.98  S2 = 4.38     Answer A. Reject H0 if 6.98/4.38 > 2.53. B. Reject H0 if 48.72/19.14 > 3.19.. C. Reject H0 if 48.72/19.14 > 2.26. D.   Reject H0 if 6.98/4.38 > 3.19.

6 Given the hypothesis and the sample data, find the decision criterion that would be used for rejecting the null hypothesis.  Assume that all populations are normally distributed.  Assume that independent random samples have been drawn from populations with unknown but equal variations. H0:  u1 = u2.   H1:  u1 ? u2.   Sample A:     n1 = 22,     x?1=178,       s1=36. Sample B:    n2 = 15,     x?2 = 290,     s2 = 41. ? = 0.05 Answer A. Reject H0 i f test statistic > 1.96 or < -1.96. B. Reject H0 i f test statistic < 1.96 or > -1.96. C.   Reject H0 i f test statistic < 1.645 or > -1.645. D. Reject H0 i f test statistic > 1.645 or < -1.645.

7 Construct a 90% confidence interval for  u1 -  u2   based on the sample data below.  Assume that all populations are normally distributed.  Assume that independent random samples have been drawn from populations with unknown and unequal variances.  Sample A:     n1 = 8,     x?1=151,       s1=31. Sample B:    n2 = 21,     x?2 = 130,     s2 = 72. Answer A.   0 < u1 -  u2 < 42 B. -15 < u1 -  u2 < 57 C.   -29 < u1 -  u2 < 71 D.   -6 < u1 -  u2 < 48

Explanation / Answer

4) A. Reject the null hypothesis if test statistic is > 2.624.

5) C. Reject H0 if 48.72/19.14 > 2.26.

6) A. Reject H0 i f test statistic > 1.96 or < -1.96

7) B. -15 < u1 -  u2 < 57

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