Homework SourseThe business college wants to know if their graduates are ge
The business college wants to know if their graduates are getting paid better than the teaching college. They take a random survey of 2 business college graduates and 2 teaching college graduates, and 2 college of nursing and report on their incomes. At a 0.05 significance level can we conclude that there is a difference in the mean income of the two groups?
Answer the following questions:
What is the treatment degrees of freedom (MST degrees of freedom)?
What is the error degrees of freedom (MSE degrees of freedom)?
What is the critical valud of the F distribution?
What is the SST?
What is the SSTotal?
What is the SSE?
What is the MST?
What is MSE?
What is the calculated value of the F distribution?
What is the decision?
Reject the null hypothesis
Fail to reject the null hypothesis
Reject the alternative hypothesis
Fail to reject the alternative hypothesis
| Reject the null hypothesis | ||
| Fail to reject the null hypothesis | ||
| Reject the alternative hypothesis | ||
| Fail to reject the alternative hypothesis |
Solution
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What is the treatment degrees of freedom (MST degrees of freedom)?
3-1=2
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What is the error degrees of freedom (MSE degrees of freedom)?
5-2=3
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What is the critical valud of the F distribution?
Given a=0.05, the critical value is F(0.95, df1=2, df2=3)=9.55 (from F table)
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What is the SST?
SST=72.3333
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What is the SSTotal?
SSTotal=103.333
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What is the SSE?
SSE=31
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What is the MST?
MST= SST/degree of freedom
=72.3333/2
=36.16665
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What is MSE?
MSE =SSE/ degree of freedom
=31/3
=10.333
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What is the calculated value of the F distribution?
F=MST/MSE
=36.16665/10.333
=3.5
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What is the decision?
Since F=3.5 is less than 9.55, we do not reject the null hypothesis.
Fail to reject the null hypothesis
| Mean | n | Std. Dev | |
| 67.0 | 2 | 4.24 | Business |
| 75.5 | 2 | 0.71 | Nursing |
| 71.5 | 2 | 3.54 | Teaching |
| 71.3 | 6 | 4.55 | Total |
