Question

“Are Women Really More Talkative Than Men?” is the title of a 2007 article that appeared in the journal Science. In the article, Mehl and colleagues report the results of a study of 396 men and women. Each par-ticipant wore a microphone that recorded every word he or she uttered. The researchers counted the number of words uttered by men and women and compared them. The data below are fictional but they re-create the pattern that Mehl and colleagues observed:

Men: 16,345 17,222 15,646 14,889 16,701 Women: 17,345 15,593 16,624 16,696 14,200

Conduct the appropriate t-test (independent or paired) to test the hypothesis that there is a difference in the number of words uttered by men versus women using a two-tailed α = .05

Calculate r2 as a measure of effect size, and state whether the effect is small, medium, or large.

Calculate the 99% confidence interval to determine whether or not the result is significant at the

the α = .01 level.

Report the your results in APA style as you would do in a journal article.

Answer 1

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

ALPHA= 0.05

Firstly we will check the assumption of independent ttest that is equality of variances.

NULL HYPOTHESIS H0:

ALTERNATIVE HYPTHESIS Ha:

F= s^2(m)/s^2(f)

F= 833596.3/1511628

F=0.551

The p-value is .711053. The result is not significant SINCE p > .05.

CONCLUSION: Since P value is not significant we fail to reject the null hypothesis and conclude that variances are equal.

where sp is pooled standard deviation

t= 0.1

P value for two tailed test = 0.922

Since P value is greater than 0.05 level of significance hence not significant.

Conclusion: Since P value is not significant we fail to reject null hypothesis and conclude that we dont have sufficient evidence to show that  there is a difference in the number of words uttered by men versus women.

r^2= t^2/(t^2+d.f)

r^2= 0.01+0.01+8

r^2= 0.0013

EFFECT SIZE IS SMALL

99% CONFIDENCE INTERVAL IS

tc is critical value

69 ± (3.36 * 684.87) = 69 ± 2297.998

CI [-2228.998, 2366.998].

You can be 99% confident that the difference between your two population means (μ1 - μ2) lies between -2228.998 and 2366.998.

Since Confidence interval contain Zero value hence not significant at 0.01 level of significance.