Question

ULA Fiduce IW 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 5 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. Spts 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

1)Two variables are:

a)Score of first year male students of some selective colleges on Psychological test done in the SSHA(Survey of Study Habits and Attitudes)

b)Score of first year female students of some selective colleges on Psychological test done in the SSHA(Survey of Study Habits and Attitudes)

2.Statistic=

$t=\frac{\bar{x}-\bar{y}}{s\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}~(s=pooled~sd=29.9942)\\ =\frac{121.3-141.1}{29.9942\sqrt{\frac{1}{20}+\frac{1}{18}}}\\=-2.03$

3.CI=(-36.07,-3.532)

Since all the values within this interval lie on the left side of zero, hence we can say the difference of mean scores between men and women is always negative with 90% confidence. Hence mean score of men is lower than mean score of women.So female students are much more serious than male students towards study habits and attitude.

4.Under normality assumption with homogeneity, we are to perform Fisher's t-test for testing

$H_{0}:\mu_1=\mu_2~\rm{vs}~H_{0}:\mu_1\neq\mu_2$

denote the mean score of men and women in the test of SSHA.

111, 112

MINITAB OUTPUT:

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 20 121.3 32.9 7.3
2 18 141.1 26.4 6.2

Difference = mu (1) - mu (2)
Estimate for difference: -19.8000
95% CI for difference: (-39.5636, -0.0364)
T-Test of difference = 0 (vs not =): T-Value = -2.03 P-Value = 0.050 DF = 36
Both use Pooled StDev = 29.9942
If we choose alpha=0.05, the p-value=alpha. Hence inconclusive for the first year students.

5.If p-value=0.047<0.05 thence reject the null hypothesis and we can say there is enough evidence to conclude that the mean score of first year female students is really different from mean score of first year male students for the selected private colleges.