Question

Do male and female students study the same amount per week? In 2007, 58 sophomore business students were surveyed at a large university that has more than 1,000 sophomore business students each year. The table beloe has the gender and hours spent studying in a typical week for the sampled students.

a. At the 0.05 significance level, is there a difference in the variance of study time for male students and female students? (1 point)

b. Using the results of part (a), which t-test is appropriate for comparing the mean study time for male and female students? (1 point)

c. At the 0.05 significance level, conduct the test selected in part (b) (1 point)

d. Write a short summary of your findings (1 point)

Gender	Study
M	10.0
F	18.0
M	5.5
F	20.0
F	10.0
F	18.0
F	8.0
M	6.0
F	25.0
F	22.5
M	14.0
M	10.0
F	30.0
M	6.0
F	20.0
M	12.0
M	21.0
M	15.0
M	12.0
M	10.0
M	8.5
M	25.0
F	24.0
M	10.0
M	20.0
M	8.0
M	8.0
M	12.0
M	6.0
M	6.0
M	7.0
F	15.0
M	10.0
M	10.0
F	15.0
F	10.0
F	14.0
F	15.0
F	12.0
M	9.0
F	11.0
M	10.0
M	30.0
M	10.0
F	12.0
M	10.0
M	5.0
F	15.0
M	5.0
M	10.0
M	11.0
M	15.0
M	15.0
M	7.0
M	8.0
M	12.0
M	10.0
F	18.0

Answer 1

a) Null and alternative hypothesis of Levene’s test:

H0: There is no difference in the variance of study time for male students and female students.

H1: There is a difference in the variance of study time for male students and female students

The P-value of Levene’s Test of equality of variances is 0.396. This is greater than 0.05. Hence we accept null hypothesis at 5% level of significance and conclude that there is no difference in the variance of study time for male students and female students.

b) The null hypothesis of Levene’s test for equal variance is accepted. Hence the first row (Equal Variance assumed) result of t test is appropriate for comparing the mean study time for male and female students.

c) Null and alternative hypothesis of t-test:

H0: There is no difference in the mean of study time for male students and female students.

H1: There is a difference in the mean of study time for male students and female students.

The P-value of t-test is 0.001. This is less than 0.05. Hence we reject null hypothesis at 5% level of significance and conclude that is a difference in the mean of study time for male students and female students.

d) The mean study time of male student is 11.026 and the mean study time of female student is 16.625. Hence we can also conclude that the mean study time of female students is higher than the mean study time of male students.