The average annual cost (including tuition, room, board, books, and fees) to attend a public college takes nearly a third of the annual income of a typical family with college-age children (Money. April 2012). At private colleges, the average annual cost is equal to about 60% of the typical family's income. The following tables show a random sample of the annual cost of attending private and public colleges. Data are in thousands of dollars.You must use Excel to solve this problem

Private colleges

$55.80

$43.20

$47.00

$33.30

$44.00

$30.60

$45.80

$37.80

$50.50

$42.00

Public colleges

$22.60

$18.00

$28.20

$15.60

$24.10

$28.50

$22.80

$25.80

$18.50

$25.60

$19.60

$21.80

a) Compute the sample mean and sample standard deviation for private and public colleges, respectively.

b) What is the point estimate of the difference (hypothesized difference) between the two population means?

c) Develop a 99% confidence interval of the difference between the annual cost of attending private and public colleges(assume that the two samples have equal variance). Show all your work.

d) Formulate the hypothesis that can be used to determine whether the sample data support the hypothesis that private colleges have a higher cost of attendance than public colleges.

e) Perform a hypothesis test using a significance level of 0.05 (= 0.05) to determine whether there is sufficient evidence to refute the hypothesis you stated in part (d).