A researcher with the Ministry of Transportation is commissioned to study the drive times to work (one-way) for U.S. cities. The underlying hypothesis is that average commute times are different across cities. To test the hypothesis, the researcher randomly selects six people from each of the four cities and records their one-way commute times to work. Refer to the below data on one-way commute times (in minutes) to work. Note that the grand mean is 36.625. The conclusion for the hypothesis test is ________.
A) to reject the null hypothesis; we cannot conclude that not all mean commute times are equal
B) do not reject the null hypothesis; we cannot conclude that not all mean commute times are equal
C) reject the null hypothesis; we can conclude that not all mean commute times are equal
D) do not reject the null hypothesis; we can conclude that not all mean commute times are equal

Question

A researcher with the Ministry of Transportation is commissioned to study the drive times to work (one-way) for U.S. cities. The underlying hypothesis is that average commute times are different across cities. To test the hypothesis, the researcher randomly selects six people from each of the four cities and records their one-way commute times to work. Refer to the below data on one-way commute times (in minutes) to work. Note that the grand mean is 36.625.  The conclusion for the hypothesis test is ________.
A) to reject the null hypothesis; we cannot conclude that not all mean commute times are equal 
B) do not reject the null hypothesis; we cannot conclude that not all mean commute times are equal 
C) reject the null hypothesis; we can conclude that not all mean commute times are equal 
D) do not reject the null hypothesis; we can conclude that not all mean commute times are equal

Quizplus · Accepted Answer

To test the hypothesis that average commute times are different across cities, we need to conduct an ANOVA test with the null hypothesis being that all four cities have the same mean commute time. The p-value obtained from the ANOVA test is less than the level of significance (assuming α=0.05), which means we reject the null hypothesis. Thus, we can conclude that not all mean commute times are equal, and the underlying hypothesis is supported.

A Researcher with the Ministry of Transportation Is Commissioned to Study