Question

You have heard that if you leave your money in mutual funds for a longer period of​ time, you will see a greater return. So you would like to compare the​ 3-year and​ 5-year returns of a random sample of mutual funds to see if​ indeed, your return is expected to be greater if you leave your money in the fund for 5 years. Complete parts a through d. Assume a significance level of

alpha

equals0.05.

3-Year_Returns
0.56
6.79
7.07
0.22
3.95
1.26
4.41
2.18
3.43
5.47
1.99
6.74
-1.08
8.14
0
-1.09
2.08
4.93
0.16
12.32
2.62
-0.26
1.72
5.26
-3.81
11.16
7.18
4.66
8.67
-0.19
6.65
3.59
2.08
5.84
-0.61

5-Year_Returns
6.05
10.78
11.34
7.83
9.59
7.27
6.56
7.67
9.72
9.82
6.08
10.77
2.19
12.99
5.21
5.08
7.49
9.44
6.95
10.03
9.39
4.15
7.24
11.71
4.43
14.28
10.82
9.39
13.74
5.77
10.45
7.97
4.67
11.73
5.84

c) Test the hypothesis and find the​ P-value.

Identify the test statistic.

tequals

nothing

​(Round to two decimal places as​ needed.)

Identify the​ p-value.

Pequals

nothing

​(Round to three decimal places as​ needed.)

Draw a conclusion for this hypothesis test.

d) Find a 95% confidence interval for the mean difference.

Answer 1

After entering the data in Excel and importing it to R we can easily perform the Analysis of two sample t - test

Let denote the mean return for 3 year old and denote the mean return for 5 year old investment

then

then test statistic will be:

Output in R is as follows

P value

and confidence interval is given above highlighted