A fashion industry analyst wants to prove that models featuring Liz Claiborne clothing earn on average more than models featuring clothes designed by Calvin Klein. For a given period of time, a random sample of 32 Liz Claiborne models reveals average earnings of $4,238.00 and a standard deviation of $1,002.50. For the same period, an independent random sample of 37 Calvin Klein models has mean earnings of $3,888.72 and a sample standard deviation of $876.05.

a. Is this a one-tailed or a two-tailed test? Explain.

b. Carry out the hypothesis test at the 0.05 level of significance.

c. State your conclusion.

d. What is the p-value? Explain its relevance.

e. Redo the problem, assuming the results are based on a random sample of 10 Liz Claiborne models and 11 Calvin Klein models.