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Significance level and arithmetic mean salaries

One reads that a business school graduate with an undergraduate degree earns more than a high school graduate with no additional education, and a person with a master's degree or a doctorate earns even more. To investigate we select a sample of 25 mid-level managers of companies with less than 200 employees. Their incomes, classified by highest level of education, follow.

Income ($ thousands)
High School or Less Undergraduate DegreeMaster's Degree or More

45 49 51
47 57 73
53 85 82
62 73 59
39 81 94
43 84 89
54 89 89
A 92 95
A 62 73

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.

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Solution Summary

This solution provides a null and alternative hypothesis and conducts a one-factor ANOVA to determine the F-statistic for comparison to the p-value. A decision is made to accept or reject the null hypothesis. It also conducts a post hoc analysis to find out which groups differ.