# Statistics - Degrees of Freedom

A political scientist obtained recordings of election-night acceptance speeches of seven newly elected representatives to the US Congress. She counted the number of minutes devoted to urban problems in these speeches. Four of the representatives were from rural districts and three were from urban districts. Listed below are the numbers of minutes devoted to urban problems by each representative based on where they were from. Do these data suggest that the amount of time devoted to urban problems in acceptance speeches of newly elected representatives to the U.S. Congress differ according to whether they come from rural or urban districts? (Use the .05 level)

Urban Rural

11 5

11 0

14 3

4

Use the information from the table above to answer the questions below:

4.What are the degrees of freedom (df) for each sample and for the total?

8.What is the estimate of the population variance from each sample?

What is the pooled estimate of the variance of the population?

11.What is the estimate of the population variance for each of the distributions of means? What is the population variance of the distribution of differences between means? What is the standard deviation of the distribution of differences between means?

14.What is the cut-off score on the comparison distribution at which the null hypothesis should be rejected?

16.What is the t-score for the differences in actual sample means?

25.What is your conclusion? State it in words and in symbols as you would for a research article.

#### Solution Summary

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