Question

In: Statistics and Probability

Companies often have different mutual funds to serve different investment time horizons. Use the tab titled...

Companies often have different mutual funds to serve different investment time horizons. Use the tab titled BESTFUNDS to determine if there is a difference between in the three-year annualized return for small cap growth, mid-cap growth, and large cap growth mutual funds.

(a) Identify which type of test you plan to use and why.

(b) Analyze and report your findings.

Small Mid-Cap Large
33.21 5.34 27.08
25.33 25.59 14.80
29.19 26.01 20.87
29.96 24.41 9.53
28.05 24.90 28.40
26.36 24.96 22.33
32.89 25.92 26.52
30.58 24.81 25.99
31.18 26.22 25.06
25.25 24.44 27.91

(c) Put the findings into meaningful words (i.e., explain what the test allows you to conclude about the types of mutual funds).

(d) Does your result from

(b) give you statistical permission to probe group differences, yes or no?

Solutions

Expert Solution

(a) The One-Way ANOVA test would be appropriate here because we have 3 levels of the independent variable.

(b) The hypothesis being tested is:

H0: µ1 = µ2 = µ3

Ha: Not all means are equal

Mean n Std. Dev
29.200 10 2.9072 Small
23.260 10 6.3303 Mid-Cap
22.849 10 6.2265 Large
25.103 30 5.9835 Total
ANOVA table
Source SS    df MS F    p-value
Treatment 252.6257 2 126.3129 4.34 .0232
Error 785.6455 27 29.0980
Total 1,038.2712 29

The p-value is 0.0232.

Since the p-value (0.0232) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that not all means are equal.

(c) We can conclude that there is a difference between in the three-year annualized return for small cap growth, mid-cap growth, and large cap growth mutual funds.

(d) yes


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