Question

Commute times in the U.S. are heavily skewed to the right. We select a random sample of 500 people from the 2000 U.S. Census who reported a non-zero commute time. In this sample the mean commute time is 27.6 minutes with a standard deviation of 19.6 minutes. Can we conclude from this data that the mean commute time in the U.S. is less than half an hour? Conduct a hypothesis test at the 5% level of significance. What can we conclude? Group of answer choices Nothing. The distribution of the variable in the population is heavily skewed, so the conditions for use of a t-model are not met. We cannot trust that the p-value is accurate for this reason. With a mean of 27.6 minutes, the data supports the claim that the average commute time is less than 30 minutes, but the difference is not statistically significant. We fail to reject the null hypothesis that the mean commute time in the U.S. in the year 2000 was 30 minutes. With a mean of 27.6 minutes, the data supports the claim that the average commute time is significantly less than 30 minutes. We reject the null hypothesis that the mean commute time in the U.S. in the year 2000 was 30 minutes.

Answer 1

With a mean of 27.6 minutes, the data supports the claim that the average commute time is significantly less than 30 minutes. We reject the null hypothesis that the mean commute time in the U.S. in the year 2000 was 30 minutes.

Explanation:

Check the attached file for a detailed explanation of the solution.

From the calculation of the test statistic, ts = - 2.738

At ts = -2.738 and df = 500 - 1 = 499, P-value = 0.0031

Since P-value is less than the significance level, the null hypothesis is rejected.