“College costs spike again” (October 19, 2005), an article that appeared on the CNN Money website, gave the latest figures from the College Board on annual tuition, fees, and room and board. The average total figure for private colleges is $27,516 and $11,354 for public colleges.

Source: http://money.cnn.com/2004/10/18/pf/college/

college_costs/

In an effort to compare those same costs in New York State, a sample of 32 students in their junior year of college is randomly selected statewide from the private colleges and 32 more students are selected from public colleges. The private college sample resulted in a mean of $27,436, and the public college sample mean was $11,147.

a. Assume the annual college fees for private colleges have a mounded distribution and the standard deviation is $1800. Find the 95%

confidence interval for the mean college costs in New York State.

b. Assume the annual college fees for public colleges have a mounded distribution and the standard deviation is $1200. Find the 95%

confidence interval for the mean college costs in New York State.

c. How do New York State college costs compare with the College Board’s values? Explain how they differ.

d. Compare the confidence intervals found in parts a and b and describe the effect the two different sample means had on the resulting answers.

e. Compare the confidence intervals found in parts a and b and describe the effect the two different standard deviations had on the resulting answers.