Question

A survey in the; N.Y. Times Almanac; finds the mean commute time (one way) is 25.4 minutes for the 15 largest US cities. The Austin, TX chamber of commerce feels that Austin’s commute time is less and wants to publicize this fact. The mean for 25 randomly selected commuters is 22.1 minutes with a standard deviation of 5.3 minutes. At the α = 0.10 level, is the Austin, TX commute significantly less than the mean commute time for the 15 largest US cities?

a) Yes, at α = 0.10, the Austin, TX commute is significantly less than the mean commute time for the 15 largest US cities.

b) No, at α = 0.10, the Austin, TX commute is not significantly less than the mean commute time for the 15 largest US cities.

c) Yes, at α = 0.10, but the significance is marginal.

d) No, at α = 0.10, but the significance is marginal.

Answer 1

To determine if the Austin, TX commute time is significantly less than the mean commute time for the 15 largest US cities, a hypothesis test can be conducted.

Step-by-step explanation:

To determine if the Austin, TX commute time is significantly less than the mean commute time for the 15 largest US cities, we can conduct a hypothesis test.

• Null hypothesis (H0): The mean commute time for Austin, TX is not significantly less than the mean commute time for the 15 largest US cities.
• Alternative hypothesis (Ha): The mean commute time for Austin, TX is significantly less than the mean commute time for the 15 largest US cities.

Step 1: Calculate the test statistic using the formula:

test statistic = (sample mean - population mean) / (sample standard deviation / square root of sample size)

Step 2: Determine the critical value using the α = 0.10 level.

Step 3: Compare the test statistic with the critical value.

If the test statistic is less than the critical value, we reject the null hypothesis and conclude that the Austin, TX commute is significantly less than the mean commute time for the 15 largest US cities.

If the test statistic is greater than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the Austin, TX commute is significantly less than the mean commute time for the 15 largest US cities.