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

# Test for departments

First of all , we have to state null and alternative hypothesis as following types:-  

Null hypothesis will be

H₀ : μ1 = μ2 = μ3

And Alternative hypothesis

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

Now, we will Formulate an analysis plan. For the analysis, the significance level is 0.05.

To Analyze sample data we calculate sample statistic as given below :-

F statistics is given by:-

F = 3.05

F(critical) = 19

And P-value = 0.2464

conclusion--   here we get the P-value (0.2464) is greater than the significance level (0.05), so we have to accept the null hypothesis (H₀ ).

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

# Test for gender

First step we have to state the null hypothesis ( H₀ ) and an alternative hypothesis ( Ha ).

Null hypothesis

H₀: μ1 = μ2

Alternative hypothesis

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

Here to Formulate an analysis ,we have the significance level is 0.05.

Now we Analyze sample data as givem below

F statistics is given by:-

F = 1.79

F (critical ) = 18.51

The P-value = 0.31

In this case our results will be :-- here the P-value (0.31) is greater than the significance level (0.05), so we have to accept the null hypothesis (H₀)

Conclusion:-

Here we have to Reject H0, There is no sufficient evidence for significant differences between the genders.

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