Question

How do private universities and public colleges compare with respect to debt at graduation incurred by students? The worksheet "CollegeDebt" contains the average debt at graduation incurred by students for 100 private universities and 100 public colleges, as reported by Kiplinger. (Data extracted from “Kiplinger’s Best College Values”)

1. At the 0.05 level of significance, is there a difference in the variance of average graduation debt incurred by students for private universities and public colleges?   Be sure to write out the hypotheses clearly in your output and to clearly state your conclusion.
2. Using the results of (a), which t test is appropriate for comparing mean debt at graduation incurred by students at private universities and public colleges? What is your conclusion for the test (using a level of significance of 0.05)?
3. Write a short summary of your findings.

Private	Public
8,908	20,852
16,702	21,645
22,256	24,598
24,122	25,712
22,497	18,789
17,849	21,323
13,625	21,900
24,954	25,338
18,219	21,507
21,987	27,559
23,463	26,400
23,389	21,730
29,217	27,831
23,593	23,679
23,810	27,530
23,577	16,577
24,536	32,169
20,481	25,718
23,852	24,811
28,406	21,830
23,412	20,759
24,267	21,001
20,308	26,644
15,158	24,072
23,550	27,930
34,215	20,466
38,605	22,413
27,882	28,884
33,797	22,058
30,742	25,222
32,922	30,136
35,545	24,656
26,870	28,039
27,385	25,975
31,046	28,147
21,500	21,911
23,367	35,798
41,098	33,150
28,194	22,337
30,170	31,579
33,299	20,432
33,649	28,407
35,921	38,612
21,474	7,915
30,866	13,000
31,210	29,012
31,642	19,276
30,700	33,816
19,266	21,081
29,292	29,956
34,655	37,213
33,305	28,444
30,561	24,784
28,249	19,500
34,136	27,715
35,346	19,915
23,753	31,397
29,640	20,201
31,077	24,182
23,225	25,322
44,540	22,026
29,291	25,112
35,730	28,617
26,181	26,487
25,725	23,001
31,011	22,582
31,181	22,760
39,584	27,405
29,646	28,170
36,132	15,165
23,984	18,685
30,698	11,275
29,601	23,553
35,000	26,685
35,421	28,162
32,108	26,283
37,753	14,383
37,910	24,213
36,278	25,732
39,775	26,964
34,423	24,252
38,226	30,451
38,988	23,231
37,571	22,251
40,307	24,420
31,020	31,188
26,643	19,969
23,500	22,903
28,294	23,665
31,993	29,959
38,198	37,708
38,992	19,727
28,880	24,699
34,844	10,062
32,208	19,444
41,272	27,045
31,644	25,542
28,297	26,940
35,925	30,132
32,862	21,217

Provide steps for each question

Answer 1

Let Private be represented by 1 and Public by 2.

Part 1: -

First step will be to find the sample variances of the two datasets using var.s() function in excel.

Part 2: now calculate sample means using average() function in excel

Summary:

There is enough evidence to conclude that the population means differ but not sufficient evidence to conclude that the population variances differ at 5% significance level.