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. Here is the t-test applet. Click here to open the applet.What can we conclude? 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.

Name: Commute times in the U.S. are heavily skewed to the right. We select a
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Description: 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

Hypothesis Testing: Hypothesis is a procedure by which we can test an assumption regarding a population parameter. And it depends on the nature of the data used and the reason for the analysis. Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. T-test: This test is extensively used for testing population means. Generally, it is used instead of the corresponding z-test when the population standard deviation is not known. Assumptions: 1. The parent population from which the sample is drawn is normal. 2. The sample observations are independent ie. the sample is random. 3. The population standard deviation is unknown. Test Statistics: t=X¯-μ0snThe given sample mean is X¯=27.6 and sample standard deviation is s=19.6 and sample size n=500 1.Null and Alternative Hypotheses: The following null and alternative hypotheses need to be tested: H1: μ=30H1: μ<30 ie. It is a left-tailed test, for which a t-test for one mean, with unknown population standard deviation, will be used. 2. Test Statistics: The t-statistic is computed as follows: t=X¯-μ0sn=27.6-3019.6500t=-2.738 3. Rejection Region: Based on the information provided, the significance level is α=0.05, and the critical value for a left-tailed test is tc=-1.648. The rejection region for this left-tailed test is R=t:t<−1.648 4. Decision:Since it is observed that t=-2.738<tc=-1.648 ie. null hypothesis is rejected. 5. Conclusion: It is concluded that the null hypothesis is rejected. Therefore, there is enough evidence to claim that the mean commute time in the U.S. is less than half an hour. Hence, Option 3 is true.

Answered: Commute times in the U.S. are heavily…

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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. Here is the t-test applet. Click here to open the applet.

What can we conclude?

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.

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