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. Use an applet to help you. Click here to open the applet in a separate window. This applet may not work on mobile devices. In the applet, you can type the degrees of freedom in the box at the top and type the t-score in the box at the bottom and the resulting area under the curve will be displayed. What can we conclude? (i) 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. (ii) 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. (iii) 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.