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Suppose our goal is to quantify the impact of the repeal of the national maximum speed limit on

average speeds on U.S. roads. Representative speed data are collected for particular time periods before and after the repeal. The spreadsheet "hw1_speed_data.csv" contains vehicular speed data before and after the repeal of a speed limit law. Use R to do the solve the following questions:

1. Generate summary statistics for vehicular speeds data and compare the results. (10)

2. Generate and interpret box plots for vehicular speeds data. Compare the plots. (10)

3. Find out the frequency distribution of vehicular speeds data and compare the results. (10)

4. Generate 99% confidence intervals for the variance of before-speed data. Explain each step and interpret the results. (10)

5. Generate 95% confidence intervals for mean vehicular after-speed data assuming the population variance is unknown. Explain each step and interpret the results. (10)

6. Test whether the mean speed is 65 mph after the repealing of the speed limit at the =5% significance level. Explain each step and interpret the results. (10)

7. Test whether the variance of before-speed data is less than 20 mph2 at the =1% significance level. Explain each step and interpret the results. (10)

8. Test that the vehicular after-speed mean is greater than before-speed at the =5% significance level. Explain each step and interpret the results. (10)

9. Test that the vehicular before-speed variance is less than after-speed variance at the =10%

significance level. Explain each step and interpret the results. (10)

10. Use a Mann-Whitney-Wilcoxon test to assess whether the distributions of before-speed and after-speed are equal. Also, draw density plots using before and after speeds data. Interpret the results based on the test and drawing.