Question

The Bureau of the Census reports the average commuting time for citizens of both Baltimore, Maryland, and Miami, Florida. To see if their commuting times appear to be any 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.   

	Miami (X1)	Baltimore (X2)
Sample size	40	40
Sample mean	28.5 min	35.2 min
Population standard deviation	7.2 min	9.1 min

At the 0.05 level of significance, can it be concluded that the commuting times are different in the winter?

a)What is the test statistic? Round to 3 decimal places.

b)What is the p-value? Round to 4 decimal places.

Answer 1

The following null and alternative hypotheses need to be tested: Ho: M1 = 42 Ha: MY = H2 This corresponds to a two-tailed test, for which a z-test for two population means, with known population standard deviations will be used.

a)

The z-statistic is computed as follows: 2 = X1 - X2 Voni+o/n2 28.5 - 35.2 7.22 /40 + 9.12 /40

b)

Based on the information provided, the significance level is a = 0.05, and the critical value for a two- tailed test is ze = 1.96. The rejection region for this two-tailed test is R = {2:21 > 1.96}

Since it is observed that 2 = 3.652 > Ze = 1.96, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p= 0.0003, and since p= 0.0003 < 0.05, it is concluded that the null hypothesis is rejected.

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