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. (You may find it useful to reference the appropriate table: chi-square table or F table)
Player 1 | 17 | 16 | 14 | 16 | 18 | 10 | 16 | 15 | 17 | 13 |
Player 2 | 18 | 5 | 14 | 21 | 16 | 18 | 6 | 17 | 18 | 22 |
a. Select the hypotheses to test whether the
players differ in consistency.
H0: σ22 / σ12 ≥ 1, HA: σ22 / σ12 < 1.
H0: σ22 / σ12 ≤ 1, HA: σ22 / σ12 > 1.
H0: σ22 / σ12 = 1, HA: σ22 / σ12 ≠ 1.
b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
c-1. Find the p-value.
p-value < 0.01
c-2. At α = 0.10, what is your
conclusion?
Do not reject H0; we can say that consistency differs between the players
Do not reject H0; we cannot say that consistency differs between the players
Reject H0; we can say that consistency differs between the players
Reject H0; we cannot say that the consistency differs between the players
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