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 explanatory variables included several high school grade summaries coded as 10 = A, 9 = A-, etc. Here are the mean high school mathematics grades for these students. Major Gender CS EO O Males 8.68 8.35 7.65 Females 9.11 9.36 8.04 Describe the main effects and interaction using appropriate graphs and calculations.

Answer 1

Solution:-

a)

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 = 11.76

F_critical = 19

The P-value = 0.0784

Interpret results. Since the P-value (0.0784) 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 = 9.27

F_critical = 18.51

The P-value = 0.093

Interpret results. Since the P-value (0.093) 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.