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 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. 30 tournament scores from events in a tour for men showed a standard deviation of 2.2181. Conduct a hypothesis test

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 7PPS
icon
Related questions
Question
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'
Transcribed Image Text: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

     H0σ12=σ22

    Ha: σ12σ22

Under the null hypothesis, the test statistic is

     F=s12s22~F(ν1,ν2;α)        where ν1=n1-1 & ν2=n2-1   =2.467222.21812   = 1.24 

  

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Equality of Variances
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill