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 15 16 18 11 15 16 16 13 15 12 Player 18 15 20 29 23 13 24 26 19 24 Click here for the Excel Data File a. Select the hypotheses to test whether the players differ in consistency. °HO: 032 / 012 s 1, HA: oz? / 012 > 1. °Ho: oz? / 012 2 1, HA: 02² / 012 < 1. °Ho: 02² / 012 = 1, HA: 02² / 012 + 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.) Test statistic C-1. Find the p-value. 0.01 s p-value < 0.02 p-value < 0.01 p-value - 0.10 0.05 s p-value < 0.10 0.02 s p-value < 0.05 C-2. At a = 0.05, what is your conclusion? Do not reject Ho; we can say that consistency differs between the players Do not reject Ho; we cannot say that consistency differs between the players Reject Ho; we cannot say that the consistency differs between the players Reject Ho; we can say that consistency differs between the players

Answer 1

For Player 1:

Sample standard deviation using excel function STDEV.S, s₁ = 2.1108

Sample size, n₁ = 10

For Player 2:

Sample standard deviation using excel function STDEV.S, s₂ = 4.9989

Sample size, n₂ = 10

α = 0.05

a) Null and alternative hypothesis:

Hₒ : σ₂²/ σ₁² = 1

H_A : σ₂²/ σ₁² ≠ 1

b) Test statistic:

F = s₂²/s₁² = 4.9989²/2.1108² = 5.608

Degree of freedom:

df₁ = n₁-1 = 9

df₂ = n₂-1 = 9

c-1) P-value :

P-value = 2*F.DIST.RT(5.6085, 9, 9) =    0.0171

0.01 < p-value < 0.02

c-2) Conclusion:

Reject Ho; we can say that consistency differs between the players