Question

A. Dr. Lightman would like to know if ratings of attraction differed due to group size for women in general. All three groups of women were given a photo of the same man, but in group 1 the women was with 20 other women, in group 2 with two other women, and in group 3 she was alone. Does attraction depend on group size for women in general?

Group 1	Group 2	Group 3
12	10	8
4	2	0
12	10	8
4	2	0
7	4	2

**Please answer as much as you can, if not all. I need this to study for a test but Im not sure if my answers are correct. Thanks!**

1. Using hand calculations or excel and the formula from the book or class find the value of SS_between and SS_within? Show all your work.
2. Calculate the F value.
3. Write out a source of the variance table.
4. What is the interpretation of the obtained value?
5. What is the conclusion in APA format?

Answer 1

(1) Null and Altemative Hypotheses The following null and alternative hypotheses need to be tested: Ha: Not all means are equal The above hypotheses will be tested using an F-ratio for a One-Way ANOVA Based on the information provided, the significance level is a0.05, and the degrees of freedom are dfi 2 and dfe 2, therefore, the rejection region for this F-test is R-FF>Fe- 3.885)

(3) Test Statistic: From the given data

Group 1 Group 2 Group 3 12 12 10 Sum- 28 5.6 224 4.099 67.2 18 3.6 132 4.099 67.2 Average- 7.8 369 4.025 64.8 St. Dev.

The between sum of squares is computed directly as shown in the calculation below: Now that sum of squares are computed, we can proceed with computing the mean sum of squares SSetzee. 44.133 MS - 22.067 between - between MSuithinSithin 199.2 dfrithin0.0 dfwithin12 Now that sum of squares are computed, we can proceed with computing the mean sum of squares M St -22.067 between - between dfrithin0.0 within Suithin190 dfwithin12 Finally, with having already calculated the mean sum of squares, the F-statistic is computed as follows MStetreen 22.067 1220 M Suithin16.6 = 1.329

Test Statistic F = 1.329

(4) Decision about the null hypothesis Since it is observed that F 1.329 Fe 3.885, it is then concluded that the null hypothesis is not rejected Using the P-value approach: The p-value is p that the null hypothesis is not rejected. 0.301, and since p 0.30120.05, it is c It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that not all 3 population means are equal, at the a 0.05 significance level.

Thus we conclude that there is no significance difference among the three sample means.