Question

Using the Retirement funds spreadsheet, please determine if there is a significant difference between the average rate of return on Large Value and Large Growth stock funds.

1. What are the two variables of interest?
2. Write a null and alternative hypothesis statement
3. At the 95% significance level, is there significant evidence of a difference between fund rate of returns?
4. Do you accept or reject the null hypothesis?
5. Based upon your answer above, provide us with a paragraph (3-4 sentence) conclusion that would be appropriate to explain the results to a senior executive that isn’t as familiar with statistics as you are!

Growth	Value
62.91	31.25
54.79	27.03
54.75	23.49
38.84	21.94
33.65	21.76
33.18	21.26
32.45	20.93
29.08	20.02
27.22	20.01
27.17	19.46
26.97	18.94
26.40	18.87
25.50	18.83
24.97	18.25
24.85	18.21
24.72	18.04
24.64	17.95
24.20	17.87
23.81	17.78
23.77	17.88
23.73	17.63
23.70	17.34
23.47	17.42
23.40	16.86
23.23	16.67
22.80	16.65
22.77	16.55
22.37	16.35
22.15	16.23
22.01	16.15
21.80	16.04
21.74	15.98
21.71	15.97
21.65	15.94
21.62	15.81
21.34	15.53
21.24	15.51
21.21	15.49
20.96	15.36
20.94	15.34
20.83	15.23
20.71	15.16
20.86	14.98
20.63	14.96
20.62	14.93
20.55	14.85
20.27	14.45
20.23	14.27
20.07	14.25
19.63	13.94
19.46	13.22
19.39	12.12
19.23	11.32
19.16	11.21
19.13	9.82
19.08
18.92
18.87
18.77
18.46
18.38
18.34
18.28
18.12
18.01
17.98
17.98
17.94
17.76
17.69
17.63
17.53
17.43
17.25
17.25
17.25
17.17
16.86
16.68
16.61
16.59
16.41
16.32
15.96
15.92
15.89
15.65
15.51
15.50
15.44
14.96
14.67
14.39
14.36
14.33
14.28
14.02
13.23
13.11
11.94
11.54
11.51
11.19

Answer 1

1. What are the two variables of interest?

The average rate of return on Large Value and Large Growth stock funds.

1. Write a null and alternative hypothesis statement

The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ ≠ µ₂

1. At the 95% significance level, is there significant evidence of a difference between fund rate of returns?

The p-value is 0.0006.

Since the p-value (0.0006) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a significant evidence of a difference between fund rate of returns.

1. Do you accept or reject the null hypothesis?

Since the p-value (0.0006) is less than the significance level (0.05), we can reject the null hypothesis.

1. Based upon your answer above, provide us with a paragraph (3-4 sentence) conclusion that would be appropriate to explain the results to a senior executive that isn’t as familiar with statistics as you are!

There is a significant difference between the average rate of return on Large Value and Large Growth stock funds.

Growth	Value
21.0431	17.0782	mean
7.9658	3.5969	std. dev.
103	55	n
	156	df
	3.96492	difference (Growth - Value)
	45.96748	pooled variance
	6.77993	pooled std. dev.
	1.13228	standard error of difference
	0	hypothesized difference
	3.502	t
	.0006	p-value (two-tailed)