The bowling scores of a professional bowler during a two-day tournament are shown below. Can you conclude that the variability of the scores is greater on the second day than on the first day? Use the $\alpha = 0.10$ level of significance.

Question

The bowling scores of a professional bowler during a two-day tournament are shown below.  Can you conclude that the variability of the scores is greater on the second day than on the first day? Use the $\alpha = 0.10$ level of significance.

Quizplus · Accepted Answer

To determine if the variability is greater on the second day, we can use a hypothesis test for the equality of variances. With a significance level of 0.10, we can perform an F-test, comparing the variance of the first day scores to that of the second day scores. If the resulting p-value is less than 0.10, we can reject the null hypothesis of equal variances and conclude that the variability is greater on the second day. Calculating the variances and performing the F-test yields a p-value of 0.020, which is less than 0.10, so we can conclude that the variability is indeed greater on the second day.

The Bowling Scores of a Professional Bowler During a Two-Day α=0.10\alpha = 0.10α=0.10

The Bowling Scores of a Professional Bowler During a Two-Day $\alpha = 0.10$