Is there any difference in the variability in golf scores for players on a women's professional golf tour and players on a men's professional golf tour? A sample of 20 tournament scores from events in atour for women showed a standard deviation of 2.4672 strokes, and a sample of 30 tournament scores from events in a tour for men showed a standard deviation of 2.2181. Conduct a hypothesis testfor equal population variances to determine if there is any statistically significant difference in the variability of golf scores for male and female professional golfers. Use a = 0.10.State the null and alternative hypotheses.Ho: 0,2 s 0,222Ha: 01> 022Ho: 01+ 02H3: 0,2 = 0,2Ha: 01%3D2Ho: 012>022222Ho: 0102H3: 0,? *Ha: 0102Find the value of the test statistic. (Round your answer to two decimal places.)Find the p-value. (Round your answer to four decimal places.)p-value%3DState your conclusion.Do not reject Ho. We cannot conclude that there is a difference in the variability of golf scores for male and female professional golfers.Reject Ho. We can conclude that there is a difference in the variability of golf scores for male and female professional golfers.Reject Ho. We cannot conclude that there is a difference in the variability of golf scores for male and female professional golfers.Do not reject Ho. We can conclude that there is a difference in the variability of golf scores for male and female professional golfers.0'

Answered: Is there any difference in the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Is there any difference in the variability in golf scores for players on a women's professional golf tour and players on a men's professional golf tour? A sample of 20 tournament scores from events in a
tour for women showed a standard deviation of 2.4672 strokes, and a sample of 30 tournament scores from events in a tour for men showed a standard deviation of 2.2181. Conduct a hypothesis test
for equal population variances to determine if there is any statistically significant difference in the variability of golf scores for male and female professional golfers. Use a = 0.10.
State the null and alternative hypotheses.
Ho: 0,2 s 0,2
2
2
Ha: 01
> 02
2
Ho: 01
+ 02
H3: 0,2 = 0,2
Ha: 01
%3D
2
Ho: 01
2
>
02
2
2
2
2
Ho: 01
02
H3: 0,? *
Ha: 01
02
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value
%3D
State your conclusion.
Do not reject Ho. We cannot conclude that there is a difference in the variability of golf scores for male and female professional golfers.
Reject Ho. We can conclude that there is a difference in the variability of golf scores for male and female professional golfers.
Reject Ho. We cannot conclude that there is a difference in the variability of golf scores for male and female professional golfers.
Do not reject Ho. We can conclude that there is a difference in the variability of golf scores for male and female professional golfers.
0'

Expert Solution

Step 1

Given: For the two samples of women and men respectively, we are given

Sample size: n₁ = 20 & n₂ = 30

Sample SD: s₁ = 2.4672 & s₂ = 2.2181

To test the difference at $α = 0.10$ in variability of the test scores of the two groups, the hypthothesis of interest is

H₀: $σ_{1}^{2} = σ_{2}^{2}$

H_a: $σ_{1}^{2} \neq σ_{2}^{2}$

Under the null hypothesis, the test statistic is

$F = \frac{s_{1}^{2}}{s_{2}^{2}} ~ F_{(ν_{1}, ν_{2}; α)} w h e r e ν_{1} = n_{1} - 1 & ν_{2} = n_{2} - 1 = \frac{2 . 4672^{2}}{2 . 2181^{2}} = 1.24$

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