Question

The Bureau of the Census reports that the average commuting time for citizens of both Baltimore, Maryland, and Miami, Florida is approximately 29 minutes (uMiami=29 and uBaltimore=29 minutes). To investigate whether their commuting times appear to be different in the winter, random samples of 40 drivers were surveyed in each city, and the average commuting time for the month of January was calculated for both cities. The results are provided below. At the 0.05 level of significance, can it be concluded that commuting times are different in the winter?

Miami Baltimore
Sample size 40 40
Sample mean 28.5 mins 35.2 mins
Population Standard Deviation 7.2 mins 9.1 mins

perform each of the following steps

a. State the hypotheses and identify the claim

b. Find the critical value(s)

C. Compute the test value

d. Make the decision

e. Summarize the results

Answer 1

To determine if the commuting times are different in the winter in Miami and Baltimore, we conduct a hypothesis test and compare the test statistic to the critical value.

Step-by-step explanation:

To determine whether the commuting times in Miami and Baltimore are different in the winter, we can conduct a hypothesis test. Let's define the hypotheses:

Null Hypothesis (H0): The average commuting times are equal in both cities (uMiami = uBaltimore).

Alternative Hypothesis (H1): The average commuting times are different in the two cities (uMiami ≠ uBaltimore).

To perform the hypothesis test, we can calculate the test statistic and compare it to the critical value.

Given that the sample sizes are large, we can use the z-test. The test statistic (z) is calculated using the formula z = (sample mean 1 - sample mean 2) / sqrt((population variance 1 / sample size 1) + (population variance 2 / sample size 2)).

After calculating the test statistic, we compare it to the critical value from the z-table at the 0.05 level of significance. If the test statistic falls in the rejection region (outside the critical value), we reject the null hypothesis and conclude that the commuting times are different in the winter.

Finally, we summarize the results and state our conclusion.