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. Based on the sample standard deviation, the one-way ANOVA assumption that is likely not met is ________.
A) the populations are normally distributed.
B) the population standard deviations are assumed to be equal.
C) the samples are independent.
D) None of these choices is correct.

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.  Based on the sample standard deviation, the one-way ANOVA assumption that is likely not met is ________.
A) the populations are normally distributed. 
B) the population standard deviations are assumed to be equal. 
C) the samples are independent. 
D) None of these choices is correct.

Quizplus · Accepted Answer

The one-way ANOVA assumption that is likely not met is the assumption of equal population standard deviations. We can see from the sample standard deviations that they are not equal, with City B having a much larger standard deviation than the other cities. This violates the assumption of homogeneity of variances.

A Researcher with the Ministry of Transportation Is Commissioned to Study