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The data for a random sample of 10 paired observations are shown in the table below. Pair Sample from Population 1 Sample from Population 2 1 19 24 2 25 27 3 31 36 4 52 53 5 49 55 6 34 34 7 59 66 8 47 51 9 17 20 10 51 55 a. If you wish to test whether these data are sufficient to indicate that the mean for population 2 is larger than that for population 1, what are the appropriate null and alternative hypotheses? Define any symbols you use. Conduct the test, part a, using a = .10. c. Find a 90% confidence interval for M. Interpret this result. d. What assumptions are necessary to ensure the validity of this analysis