To conduct an ANOVA hypothesis test, we must check the following assumptions:

1. Random Sampling Assumption

   • The scenario does not specify that the participants were randomly selected.
     Correct Answer:
     ✅ The random sample requirement is not met because the scenario description does not specify that random samples were used.

2. Normality Assumption

   • ANOVA assumes that the data in each group follows an approximately normal distribution.
   • To determine this, we would need to construct histograms or perform normality tests (e.g., Shapiro-Wilk test).
   • Without seeing the histogram, we cannot confirm normality.
     Potential Correct Answer:
     ✅ The data normality requirement is not met because the histogram for one or more groups is extremely skewed or not normal. (If normality is violated)
     ✅ The data normality requirement is met because the histogram for each group is approximately normal. (If normality holds)

3. Equal Variance Assumption (Homogeneity of Variances)

   • ANOVA requires that the variances in the different groups are roughly equal.
   • The rule of thumb is that the largest variance should be no more than four times the smallest variance.
   • We would need to compute the variances for each group to check this condition.
     Potential Correct Answer:
     ✅ The equal variances requirement is met because the largest variance is smaller than four times the smallest variance. (If variance holds)
     ✅ The equal variances requirement is not met because the largest variance is greater than four times the smallest variance. (If variance is violated)

Would you like me to compute the variances and normality for confirmation?

Related Questions:

1. What are the consequences of violating the normality assumption in ANOVA?
2. How do we test for homogeneity of variances in ANOVA?
3. What alternative tests can be used if ANOVA assumptions are violated?
4. How can we visualize the normality of a dataset?
5. What is the interpretation of an ANOVA p-value?

Tip:

If assumptions are violated, non-parametric alternatives like the Kruskal-Wallis test can be used instead of ANOVA.