Question

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2. (17 pts total) Research has shown that people find symmetrical faces more attractive than faces that are not symmetrical. For example, a psychologist selected a random sample of 12 people and used random assignment to place them in 1 of 3 conditions. Depending on their condition assignment, participants were shown one of three pictures: a face that is perfectly symmetrical, a face that is slightly asymmetrical, and a face that is highly asymmetrical. The researcher then asked them to rate the face in terms attractiveness on a scale from 1 to 7 with 7 being the most attractive. Use the provided steps (a-f) to conduct a one-factor between subjects ANOVA that tests whether there are any differences in the attractiveness ratings across the three conditions. Perfectly Slightly Highly Symmetrical Asymmetrical Asymmetrical 7 5 5 4 6 3 5 5 M 5.75 4.25 2.75 0.96 0.96 0.50 تم لا نما لیا S a. State the hypotheses. (2 pts) b. Determine the critical value for an alpha level of 0.05. (1 pt) c. Complete the following ANOVA Summary Table. Be sure to show all work including all of the formulas on a separate sheet of paper. (7 pts) SS df MS F= Source Between Groups Within Groups Total

Answer 1

Answer:-

Given that:-

	Group1	Group2	Group3	Total
Count1	4	4	4	12
Mean,Sum/n	5.75	4.25	2.75
Standard deviation,s	0.96	0.96	0.50

a)Null and Alternative Hypothesis:

At least one mean is different.

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b)Number of treatement ,k=3

Total sample Size, N=12

df(between)=k-1=2

df(within)=N-k=9

df(total)=N-1=11

Critica value Fc =F.INV.RT(0.05,2,9)=4.256

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c)SS(between)=

SS(within)

SS(total)=SS(between)+SS(within)=24.25

MS(within)=SS(within)/df(within)=0.6944

F=MS(between)/MS(within)=12.96

Decision:Reject null hypothesis.

ANOVA
Source of Variation	SS	df	MS	F
Between Groups	18	2	9	12.96
Within Groups	6.25	9	0.69
Total	24.25	11

d)Eta,SS(between)/SS(total)=18/24.25=0.7423

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