Question

9. Mutual funds mix different types of investments which alters performance. Use the tab titled BESTFUNDS1 to determine if there is a difference between the one-year and three-year annualized return for the 20 mutual funds shown in the file. (a) Identify which type of test is most appropriate for you to use, justify your answer. (b) Determine whether or not the mean return differs for the two investment horizons (use α = .05). (c) Make sure to interpret the results for real-world use (i.e., explain what the test allows you to conclude about the mutual funds). (3 points)

Mutual Fund	One-Year return	Three-Year Return
Mutual Fund 1	2.4	4.5
Mutual Fund 2	2.5	3.5
Mutual Fund 3	7.4	7.4
Mutual Fund 4	15.9	5.3
Mutual Fund 5	7.0	19.2
Mutual Fund 6	18.2	14.3
Mutual Fund 7	18.0	26.7
Mutual Fund 8	5.2	22.8
Mutual Fund 9	17.2	9.6
Mutual Fund 10	18.7	9.3
Mutual Fund 11	9.8	20.3
Mutual Fund 12	17.7	27.6
Mutual Fund 13	12.1	19.3
Mutual Fund 14	11.2	21.6
Mutual Fund 15	4.0	8.0
Mutual Fund 16	21.6	11.7
Mutual Fund 17	6.5	8.2
Mutual Fund 18	7.0	13.9
Mutual Fund 19	10.4	10.8
Mutual Fund 20	4.1	17.6

Answer 1

(a) We have two years data of returns and both the years are dependent or correlated to eachother therefore the data is paired. Hence paired t test is appropriate for this type of problem.

(b)  

(c) The hypothesis for the test would be

H0: There is no statistically significant difference in mean return of first and third year.

Ha: There is statistically significant difference in mean return of first and third year.

As we can see from the output of the paired sample t test, we found the p-value is 0.099 which is greater than the level of significance 0.05 therefore we fail to reject the null hypothesis and concluded that there is no statistically significant difference in mean return of first and third year.