Two basketball players on a school team are working hard on consistency of their
ID: 3353908 • Letter: T
Question
Two basketball players on a school team are working hard on consistency of their performance. In particular, they are hoping to bring down the variance of their scores. The coach believes that the players are not equally consistent in their games. Over a 10-game period, the scores of these two players are shown below. Assume that the two samples are drawn independently from normally distributed populations. Use Table 4.
a.
Select the hypotheses to test whether the players differ in consistency.
b.
Calculate the value of the test statistic. Remember to put the larger value for sample variance in the numerator. (Round your answer to 2 decimal places.)
c-1.
Calculate the critical value at the 10% significance level. (Round your answer to 2 decimal places.)
Two basketball players on a school team are working hard on consistency of their performance. In particular, they are hoping to bring down the variance of their scores. The coach believes that the players are not equally consistent in their games. Over a 10-game period, the scores of these two players are shown below. Assume that the two samples are drawn independently from normally distributed populations. Use Table 4.
Explanation / Answer
The statistical software output for this problem is:
Two sample variance hypothesis test:
12 : Variance of Player 2
22 : Variance of Player 1
12/22 : Ratio of two variances
H0 : 12/22 = 1
HA : 12/22 1
Hypothesis test results:
Hence,
a) Hypotheses: H0: 22 / 12 = 1, HA: 22 / 12 1
Option B is correct.
b) Test statistic = 3.30
c) Critical value = 3.18
Ratio Num. DF Den. DF Sample Ratio F-Stat P-value 12/22 9 9 3.3021845 3.3021845 0.0898