# Calculating P-value and F test

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One reads that a business school graduate with an undergrad degree earns more than a high school grad with no additional ed, and a person with a master's or a doctorate earns even more.

To test this a random sample of 25 executives from compainies with assests over 1 million were selected. Their incomes, classified by highest level of education are in the attachement. Test at the .05 level of significance that there is no difference in the arithmetic mean salaries of the three groups. If the null hypothesis is rejected, conduct further tests to determine which groups differ.

a. What can we say about the P-value?

B. Which if any, mean salary is different from the others? Can the F test tell you this?

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##### Solution Summary

One reads that a business school graduate with an undergrad degree earns more than a high school grad with no additional ed, and a person with a master's or a doctorate earns even more.

To test this a random sample of 25 executives from compainies with assests over 1 million were selected. Their incomes, classified by highest level of education are in the attachement. Test at the .05 level of significance that there is no difference in the arithmetic mean salaries of the three groups. If the null hypothesis is rejected, conduct further tests to determine which groups differ.

a. What can we say about the P-value?

B. Which if any, mean salary is different from the others? Can the F test tell you this?

##### Solution Preview

highschool => x

<br>undergrade => y

<br>master => z

<br><x> = 49

<br>sx^2 = 61

<br>sx = 7.81

<br>d.f. = nx - 1 = 7 - 1 = 6

<br>t(alpha/2) = t(.05/2) = 2.447

<br>

<br><y> = 74.67

<br>sy^2 = 234.25

<br>sy = 15.31

<br>d.f. = 8

<br>t(.025) = 2.306

<br>

<br><z> = 78.33

<br>sz^2 = 242.75

<br>sz = 15.58

<br>d.f. = 8

<br>t(.05/2) = ...

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