Final answer:
To determine if the Austin commute is significantly less than the mean commute time for the 15 largest U.S. cities, a one-sample t-test can be used. The sample mean, sample standard deviation, and sample size are used to calculate the t-value, which is then compared to the critical value. If the t-value is less than the critical value, the null hypothesis is rejected.
Step-by-step explanation:
The question is about comparing the mean commute time in Austin, TX to the mean commute time of the 15 largest U.S. cities. The mean commute time for Austin commuters is 22.1 minutes with a standard deviation of 5.3 minutes. The significance level is α = 0.10. To determine if the Austin commute is significantly less than the mean commute time for the 15 largest U.S. cities, we can use a one-sample t-test. We compare the sample mean to the population mean and consider whether the difference is statistically significant.
1. Null Hypothesis: The Austin commute time is not significantly less than the mean commute time for the largest U.S. cities. μAustin ≥ μ15 largest cities
2. Alternative Hypothesis: The Austin commute time is significantly less than the mean commute time for the largest U.S. cities. μAustin < μ15 largest cities
3. Calculate the t-value using the sample mean, population mean, sample standard deviation, and sample size.
4. Compare the t-value to the critical value from the t-distribution table with (n - 1) degrees of freedom and the specified significance level. If the t-value is less than the critical value, we reject the null hypothesis and conclude that the Austin commute is significantly less than the mean commute time for the 15 largest U.S. cities.