In a study of student loans at four-year colleges across the US, the national average was found to be $29,411. You are sure that your school has a lower average of the amount that students need to borrow to complete a degree at your school. You make a claim that a student can graduate with an average debt lower than the national average. To test your claim, you use data from a random sample of recent graduates from your school. The data is in the attached file. At α = 0.05, is there enough evidence to support your claim? Be sure to show the following information:

Null and alternative hypotheses in appropriate symbolic form

Test statistic

P-value.

For the hypotheses you specified, there are two errors that could occur:

Concluding that the student loan average at your school is lower than the national average, when it is not.

Concluding that the student loan average at your school is not lower than the national average, when it is.

Determine which of the above two errors is a Type I error and which is a Type II error. Indicate which error would have worse consequences and why.

How could the hypothesis test be conducted in order to reduce the chance of making the more serious error?

The data from the attached file:
Amount borrowed:
41685
36969
22518
23374
28298
19845
29501
32351
43035
25400
36368
31678
33266
30147
30895
30933
25687
30306
26564
24368
14208
28663
28281
33745
34679
23273
27283
35138
30256
16183
23629
13239
17167
21593
24961
31567
27611
33308
30949
30589
8784
22265
9124
31530
32515
23809
27286
28919
34057
31052
26937
31027
23435
32817
24378