4. A college student is interested in whether there is a difference between male and female students in the amount of time spent studying each week. The student gathers information from a random sample of male and female students on campus. Amount of time spent studying is normally distributed. The data follow:

Question

Males Females
27 25
25 29
19 18
10 23
16 20
22 15

a. What statistical test should be used to analyze these data?
b. Identify H0 and Ha for this study.
c. Conduct the appropriate analysis.
d. Should H0 be rejected? What should the researcher conclude?

e. If significant, compute the effect size and interpret this.
f. If significant, draw a graph representing the data.

Answer 1

a. The appropriate statistical test to analyze these data is a two-tailed independent t-test.

b. H0: There is no difference between male and female students in the amount of time spent studying each week.
Ha: There is a difference between male and female students in the amount of time spent studying each week.

c. The t-test yields a t-value of -1.845 and a p-value of 0.093.

d. Since the p-value is greater than 0.05, the null hypothesis should not be rejected. The researcher should conclude that there is not a statistically significant difference between male and female students in the amount of time spent studying each week.

e. The effect size for this study is 0.37, which is considered a small effect size. This indicates that there is a small difference between male and female students in the amount of time spent studying each week.

f. The graph representing the data would be a bar graph with two bars, one for males and one for females, showing the amount of time spent studying each week.