Suppose a researcher collected data to compare whether dogs of different size categories differed in mean cost to a pet owner. Dogs were categorized as small, medium, or large. Cost was calculated as the average annual amount spent on food, veterinary visits, and medications. The calculated F- statistic was 421.58. Given this test statistic, which of the following is the most reasonable conclusion?
A)The F- statistic shows that variation between groups is larger than variation within groups, therefore, the researcher will likely conclude that there is an association between dog size and mean cost to the pet owner.
B)The F- statistic shows that large dogs have a significantly higher cost to the pet own than the other categories, therefore, the researcher will conclude that there is an association between dog size and mean cost to the pet owner.
C)The F- statistic shows that variation within groups is larger than variation between groups, therefore, the researcher will likely conclude that there is not an association between dog size and mean cost to the pet owner.
D)None of these

Question

Quizplus · Accepted Answer

The F-statistic is a measure of the ratio of the variance between groups to the variance within groups. A large F-statistic indicates that there is more variation between groups than within groups, which suggests that there is an association between the independent variable (dog size) and the dependent variable (mean cost to the pet owner).

Suppose a Researcher Collected Data to Compare Whether Dogs of Different