Question

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?

Answer 1

(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

H_a: 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