# ANOVA and the F statistic at the 0.01 significance level.

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ANOVA and the F statistic at the 0.01 significance level.

#3) The General Social Survey is an annual survey given to a random selection of about 1500 adults in the United States. Among the many questions asked are "What is the highest level of education you've completed?" and "If you're employed full-time, how many hours do you spend working at your job during a typical week?"

We're interested in examining whether or not there are differences in the typical work week length based on the level of education of the worker. We perform a one-way, independent-samples ANOVA test, with the "groups" in the ANOVA being categories of highest educational degree of the worker ("less than high school," "bachelor's degree," etc.) and the variable being the number of hours written down by the worker in answering the survey question.

Suppose that the results of our ANOVA are given in the ANOVA table below. Complete the missing cell of the ANOVA table (rounding your answer to two decimal places), and then answer the questions below the table.

Source of Degrees of Sum of Mean F

Variation Freedom Squares Squares Statistic

Treatments 4 1451.9 363 ???

Between Groups

Error with-in 1155 106857.4 92.5

Groups

Total 1159 108309.3

How many groups (categories of highest degree earned) of respondents were examined in the ANOVA?

For the ANOVA test, it is assumes that the population variance of hours worked per week is the same for each population of workers represented. What is an unbiased estimated of this common population variance based on the sample variances?

What is the P-value corresponding to the F statistic for the ANOVA test?

From the survey data can we conclude that at leas one of the populations differs significantly from the others in mean hours worked in a typical week? Use the 0.01 level of significance. Yes or No?

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#### Solution Summary

ANOVA and the F statistic at the 0.01 significance level.