Final answer:
The correct scenario for ANOVA F-test usage is C) comparing hours working at a job for high school student athletes in three sports, given that assumptions of normality, independence, and equal variances are met. For the student's homework frequency question, ANOVA could be used if comparing more than two nights.
Step-by-step explanation:
The student is asking about which scenarios are potential candidates for the use of the ANOVA F-test, a statistical method used to compare the means of three or more groups to see if at least one is significantly different from the others. Among the given scenarios, the potential candidates for the ANOVA F-test include:
- C) We compare hours working at a job for high school student athletes in three sports (basketball, track, and soccer.)
This scenario fits the criteria for ANOVA because it involves comparing means across more than two groups (three sports), where the factor (type of sport) is a categorical variable, and hours working is a numerical response variable. Assuming that each sample is drawn from normally distributed populations with equal variances, and the samples are independent and randomly selected, the one-way ANOVA hypothesis test can be used to test the null hypothesis that the mean hours of work are equal across all sports against the alternative hypothesis that at least one of the means of hours of work is different.
For a scenario looking at nights for the highest number of students doing the majority of their homework, if it involves multiple nights (more than two), then one-way ANOVA could be appropriate. This test would examine whether the average frequency of nights when homework is done is equal for all days of the week. However, verifying assumptions such as normality, independence, and equality of variances is necessary before proceeding.