Question

9. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200. A selective private college gives the SSHA to a simple random sample of both male and female first-year students to study the difference in mean attitudes towards school and study habits between men and women. The data for men and women:

	n		s
Men	20	121.3	32.85
Women	18	141.1	26.44

1. Identify the variable of interest – be specific. (5pts)
2. Calculate the statistic for this sample. Include notation (5pts)
3. Given a 90% confidence interval for the difference of mean attitude towards school and study habits between men and women is ( -36.07 , -3.532)

Interpret the results of the confidence interval in the context of the problem. Then answer the question “Is it plausible that the mean attitudes towards school and study habits between men and women are equal?” (use complete sentences and justify your answer) 5pts

4. Most studies have found that the mean SSHA score for women is different than the mean score in a comparable group of men. Is this true for first-year students at this college that the mean SSHA score is different for women than men? Determine and state the appropriate hypotheses. 5pts
5. Given the p value is 0.047, formulate a conclusion from the results of the hypothesis test in context of the problem. (5pts)

Answer 1

Given a 90% confidence interval for the difference of mean attitude towards school and study habits between men and women is ( -36.07 , -3.532) . It does not include zero therefore SIGNIFICANT . THERE IS DIFFERENCE IN MEANS.

Testing for Equality of Variances

A F-test is used to test for the equality of variances. The following F-ratio is obtained:

FF=​s1^2/s2^2​​=(32.85)^2/(26.44)^2

The critical values are FL​=0.946 and FU​=1.067, and since F=1.544, then the null hypothesis of equal variances is rejected.

Using the P-value approach: The p-value is p=0.0472, and since p=0.0472<0.1, it is concluded that the null hypothesis is rejected.

Conclusion: It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean μ1​ is different than μ2​, at the 0.1 significance level.