Please include formulas used to answer the questions. Thanks.

QUESTION:

The SAT subject tests in chemistry and physics for two groups of 15 students each electing to take these tests are given below.

Chemistry Physics

x-bar=644 x-bar=658

s = 114 s = 103

n = 15 n = 15

a. To use the two-sample t test with a pooled estimate of 2, you must assume that the two population variances are equal. Test this assumption using the F test for equality of variances. What is the approximate p-value for the test?

b. Construct a 90% confidence interval for the variance ratio.

c. Now use the two-sample t test to detect a difference between the two population means. State the null and alternative hypotheses for the test. Test using = 0.01 and state your conclusions.

d. Find the approximate p-value for the test.

e. Find a 99% confidence interval for (mu1mu2). Interpret the interval.