Question

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).

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	1.6	4.0
Mutual Fund 4	3.0	6.8
Mutual Fund 5	4.7	5.3
Mutual Fund 6	2.0	6.9
Mutual Fund 7	3.4	5.8
Mutual Fund 8	4.3	6.4
Mutual Fund 9	3.2	5.5
Mutual Fund 10	1.6	3.8
Mutual Fund 11	13.8	20.3
Mutual Fund 12	17.7	20.3
Mutual Fund 13	13.4	19.3
Mutual Fund 14	11.2	21.6
Mutual Fund 15	4.0	8.0
Mutual Fund 16	22.1	11.7
Mutual Fund 17	6.5	8.2
Mutual Fund 18	7.0	8.5
Mutual Fund 19	10.4	10.8
Mutual Fund 20	4.1	11.3

(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).

Answer 1

(a) The paired t-test is appropriate here because each mutual fund is tested twice.

(b) The hypothesis being tested is:

H₀: µ_d = 0

H_a: µ_d ≠ 0

6.9450	mean One-Year return
9.6250	mean Three-Year Return
-2.6800	mean difference (One-Year return - Three-Year Return)
3.9730	std. dev.
0.8884	std. error
20	n
19	df
-3.017	t
.0071	p-value (two-tailed)

The p-value is 0.0071.

Since the p-value (0.0071) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the mean return differs for the two investment horizons.

(c) Thus, we can say that mutual funds mix different types of investments alters performance.