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Every city has design specifications for streets, including minimum right of way, minimum vertical grade, and minimum centerline radii on curves. Independent random samples of city streets were obtained from Washington, D.C., and New York City, and the width (in feet) of a randomly selected section was recorded. The data are given in the following table.

805_Table 06.jpg

a. Conduct a two-sample t test to determine whether there is any evidence to suggest that the population mean street widths are different. Assume the population variances are equal and use a = 0.05. Find the exact p value associated with this test.

b. Conduct a one-way analysis of variance test to determine whether there is any difference among the k = 2 population mean street widths due to city. Use a = 0.05. Find the exact p value associated with this test.

c. What is the relationship between the value of the test statistic in part (a) and the value of the test statistic in part (b)? How are the p values related? Why do these relationships make sense?

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