The IQ scores of a sample of 15 boys randomly selected from the population of fifteen year-old boys in Victoria were recorded, and the sample mean and sample standard deviation from this sample were 106 and 4, respectively.The IQ scores of a sample of 12 girls randomly selected from the population of fifteen year-old girls in Victoria were recorded, and the sample mean and sample standard deviation from this sample were 114 and 5, respectively. Let11denote the mean IQ score forfifteen year-old boys in Victoria and let22denote the mean IQ score forfifteen year-old girls inVictoria. Researchers want to test, at the 5% level of significance, the null hypothesisH0:12=1H0:12=1vs the alternative hypothesisHa:121Ha:121.Assume the population standard deviations of the two groups are equal and that the assumptions of a two-independent sample t-test are satisfied. Answer the following questions.

a. What is the test statistic and its distribution for the hypothesis test stated in the preamble of Section E

b.What is the decision rule for the hypothesis test stated in the preamble of Section E

c.What is the 98% confidence interval for12