Question

A study of undergraduate computer science students examined changes in major after the first year. The study examined the fates of 256 students who enrolled as first-year students in the same fall semester. The students were classified according to gender and their declared major at the beginning of the second year. For convenience we use the labels CS for computer science majors, EO for engineering and other science majors, and O for other majors. The mean SAT mathematics scores for the students are summarized in the following table.

	Major
Gender	CS	EO	O
Males	628	618	589
Females	582	631	543

Summarize the results of this study using appropriate plots and calculations to describe the main effects and interaction.

Answer 1

Answer:

Test for departments

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: μ1 = μ2 = μ3

Alternative hypothesis: At-least one of the μ is not equal.

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data.

F statistics is given by:-

F = 3.05

Fcritical = 19

The P-value = 0.2464

Interpret results. Since the P-value (0.2464) is greater than the significance level (0.05), we have to accept the null hypothesis.

Conclusion:-

Reject H0, There is no sufficient evidence for significant differences between the three departments.

Test for genders

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: μ1 = μ2

Alternative hypothesis: At-least one of the μ is not equal.

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data.

F statistics is given by:-

F = 1.79

Fcritical = 18.51

The P-value = 0.31

Interpret results. Since the P-value (0.31) is greater than the significance level (0.05), we have to accept the null hypothesis.

Conclusion:-

Reject H0, There is no sufficient evidence for significant differences between the genders.