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	17	12	11	15	17	12	11	18	11	17
Player 2	21	15	8	20	27	16	18	24	15	23

Click here for the Excel Data File

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.

Answer 1

Ans a ) the null and alternative hypothesis are '

H0: σ22 / σ12 = 1,  HA: σ22 / σ12 ≠ 1.

using excel>addin>phstat>two sample test

we have

F Test for Differences in Two Variances
Data
Level of Significance	0.05
Larger-Variance Sample
Sample Size	10
Sample Variance	5.498485
Smaller-Variance Sample
Sample Size	10
Sample Variance	2.960856
Intermediate Calculations
F Test Statistic	1.8571
Population 1 Sample Degrees of Freedom	9
Population 2 Sample Degrees of Freedom	9
Two-Tail Test
Upper Critical Value	4.0260
p-Value	0.3701
Do not reject the null hypothesis