4 The Department of Education reported that Stafford loan bo

4. The Department of Education reported that Stafford loan borrowers will owe, after graduation, a sample average of $42,168 with a population standard deviation of $5,400. This information was based on a random sample of 64 students. The confidence level is 99%. (7 pts)   
a. What is the standard error of the mean? b. Is the sampling distribution of xbar normally distributed? Explain. c. What is the lower limit for the interval of µ? d. What is the upper limit for the interval of µ? e. If $42,000 is the actual population mean, does it fall within the interval limits? f. If $45,000 is the actual population mean, does it fall within the interval limits?

Solution

a)

SD = 5400 / srqt 64

SD = 675

b)

Yes, because it come from from a normal distribution, and also because is a sample distribution with n larger

c)

alpha = 1- 0.99 = 0.01

alpha/2 = 0.005

Z=2.57

42168 +/- 2.57 *675

42168 +/- 1734.75

lower liimt : 40433.25

upper limit : 43902.75

e) Yes it fall in the limits

f) no it fall outside of the limits