Question

A recent study has been published concerning the effects of sugar on happiness. One group of 10 people are assigned a high sugar diet, another group of 10 people are assigned a moderate-high sugar diet, another group of 10 people are assigned a moderate-low sugar diet, and a final group of 10 people are assigned a low sugar diet. If I found that my SS_Total was 420 and my SS_Between was 255:

a. Identify the name of the test you will be employing (4 points).

b. Conduct a formal null hypothesis significance test, making sure to include every step and to show all of your work, making sure to state the hypotheses in words and using statistical notation (14 points). If you need specific symbols, we have put some here for you to copy and paste into your text entry box answer: > < ≥ ≤ = ≠ ± + - x Σ x̄ x̂ ȳ ŷ y’ μ H₀ H₁

c. Would you recommend any further statistical tests? If so, what would you recommend (please specify all tests, how many, and what each tests)? If not, why not? (1.5 points)

Answer 1

(a) One-Way ANOVA test

(b) The hypothesis being tested is:

H0: µ1 = µ2 = µ3 = µ4

Ha: At least one means is not equal

Source	SS	df	MS	F	p-value
Treatment	255	3	85	18.54545	0.0000
Error	165	36	4.583333
Total	420	39

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that at least one means is not equal.

(c) Yes, a post hoc analysis would be recommended to see which groups differ exactly.

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