8.54 Alice Chang and her colleagues (A. Chang, T. L. Rosenthal, R. H. Bryant, R. H. Rosenthal, R. M. Heidlage, and B. K. Fntzlcr. "Comparing High School and College Students' L.eisure In- wrests and Stress Ratings," Behavioral Research Therapy 31(2), 1993) tested 559 high school students using a leisure-interest checklist (LIC) survey. The means and standard deviations for each of the seven LIC factor scales are given in the following table for n = 252 male students and n = 307 female students.
a Give a 95% confidence interval for the difference in the means for male and female students for the cultural activity scale. Interpret this interval.
b Find a 90% confidence interval for the difference in the means for male and female students for the social fun factor activity.
c Do the means for males and females for the two LIC activities considered in (a) and (b) appear to differ?
Please see the attached file.
(a) For a 95% confidence level, z=1.96. By a formula, we can get a 95% CI of the difference in the means of male and female students for the cultural activity as follows
Means and Confidence Intervals are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.