Question

The Growth fund managers always claim that their portfolio yields higher rate of return compared to the value funds.In order to study if 3 YR returns of growth funds are significantly greater than those of the value funds, random samples were taken from each set of funds, Sample values are given below:

(a) Formulate the hypotheses for testing this

(b) Conduct the test and make appropriate conclusions. (Do not use ANOVA)

(c) What assumptions were made for this analysis?

Growth	Value
15.32	11.98
14.99	11.93
14.00	10.69
13.91	9.99
13.73	9.98
12.23	9.96
11.66	9.94
11.62	9.72
11.16	9.34
10.99	9.30
9.96	8.61
9.96	8.61
9.95	7.79
9.53	7.51
9.51	7.49
9.50	7.39
9.19	6.90
9.15	8.90
9.11	6.88
9.09	6.05
8.22	6.04
8.14	8.01
8.11	5.57
8.09	5.53
8.06	5.47
8.03	5.45
7.79	5.43
7.54	5.42
7.49	5.32
7.12	4.59
7.08	4.47
6.75	4.28
6.70	4.18
6.25	4.15
6.14	4.06
6.10	3.90
6.09	3.78
6.00	3.89
6.00	3.83
5.91	3.06
5.91	2.61
5.84	2.55
5.80	1.95
5.77	1.94
5.67	1.85
5.39	1.65
5.35	1.33
5.34	-2.65
4.29	-0.99
4.23
4.15
4.13
3.94
3.20
3.16
3.03
2.06
2.01
1.77
1.35
1.31
0.77
0.18
-3.40

Answer 1

first, we have to find the sample mean and standard deviation of both the groups

Sample 1: For VALUE:

Sample 2: For GROWTH:

a) Let the Value group be the sample 1

and Growth be the sample 2

b) We will conduct a t-test for two means since the population standard deviation for the two groups is not given

significance level be 0.05

hence we have enough evidence to support the claim that growth funds portfolio yields a higher rate of return compared to the value funds

c) The following assumptions have been made.

The two populations have the different variance.

The populations are normally distributed.

Each value is sampled independently from each other value.