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. (You may find it useful to reference the appropriate table: chi-square table or F table)

Player 1	12	15	18	18	14	12	16	15	20	20
Player 2	19	19	29	27	15	21	22	28	17	19

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a. Select the hypotheses to test whether the players differ in consistency.

• H₀: σ₂² / σ₁² = 1, H_A: σ₂² / σ₁² ≠ 1.

• H₀: σ₂² / σ₁² ≥ 1, H_A: σ₂² / σ₁² < 1.

• H₀: σ₂² / σ₁² ≤ 1, H_A: 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 0.10
• 0.05 p-value < 0.10
• 0.02 p-value < 0.05
• 0.01 p-value < 0.02

• p-value < 0.01

c-2. At α = 0.05, what is your conclusion?

• Do not reject H₀; we can say that consistency differs between the players

• Reject H₀; we cannot say that the consistency differs between the players

• Reject H₀; we can say that consistency differs between the players

• Do not reject H₀; we cannot say that consistency differs between the players

Answer 1