Millions of investors buy mutual funds, choosing from thousand of possibilities. some funds can be purchased directly from banks or other financial institutions while others must be purchased through brokers, who charge a fee for this service. this raises the question, can investors do better by buying mutual funds directly than by purchasing mutual funds through brokers? to answer this question, a group of researchers randomly sampled the annual returns from mutual funds that can be acquired directly and mutual funds that are bought through brokers and recorded the net annual return, which are the returns on investment after deducting all relevant feeds. a. set the hypothesis. b. implement f-test. c. implement t-test. d. what is your conclusion? explain.

direct broker
9.33 3.24
6.94 -6.76
16.17 12.8
16.97 11.1
5.94 2.73
12.61 -0.13
3.33 18.22
16.13 -0.8
11.2 -5.75
1.14 2.59
4.68 3.71
3.09 13.15
7.26 11.05
2.05 -3.12
13.07 8.94
0.59 2.74
13.57 4.07
0.35 5.6
2.69 -0.85
18.45 -0.28
4.23 16.4
10.28 6.39
7.1 -1.9
-3.09 9.49
5.6 6.7
5.27 0.19
8.09 12.39
15.05 6.54
13.21 10.92
1.72 -2.15
14.69 4.36
-2.97 -11.07
10.37 9.24
-0.63 -2.67
-0.15 8.97
0.27 1.87
4.59 -1.53
6.38 5.23
-0.24 6.87
10.32 -1.69
10.29 9.43
4.39 8.31
-2.06 -3.99
7.66 -4.44
10.83 8.63
14.48 7.06
4.8 1.57
13.12 -8.44
-6.54 -5.72
-1.06 6.95