The Survey of Study Habits as well as Attitudes (SSHA) is a psychological test designed to measure the motivation, study habits, as well as attitudes toward learning of college students. These factors, along with capability, are vital in explaining successes in school. Scores on the SSHA range from 0 to 200.
A selective private college provides the SSHA to simple random samples of both male and female first year students.
The data for the women are as follows: 154 109 137 115 152 140 154 178 101 103 126 126 137 165 165 129 200 148.
The data for the men are as follows: 108 140 114 91 180 115 126 92 169 146 109 132 75 88 113 151 70 115 187 104.
Suppose that the standard deviation for both populations is the same and use the pooled variance.
1. Obtain the P-value of the test
2. At significance level 0.05 is there significant evidence that the mean SSHA score for men is lower than the mean score in a comparable group of women?
3. Provide a left endpoint (lower limit, lower boundary) of 90% confidence interval for the mean difference (M1 - M2) between the SSHA scores of male as well as female first-year students. (M1 - the mean SSHA score for men, M2 - the mean SSHA score for the women)