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The Problem: Members of the Town of Colonie Golfers' Loop frequently raise concerns to Mr. Lange, as its leader, about how the league is run. The most frequent concern raised is that the teams competing each week are not statistically even. In other words, members raise concerns that one or more teams have a statistical advantage over other teams. To evaluate the validity of these claims, Mr. Lange has decided to use a mix of statistical hypothesis tests discussed in this course to evaluate the teams from Outing #14 in calendar-year 2016 (2016, #14). One is the Equal Vari- ances F Test, one is Welch's T Test, and the other is the 2-Sample T Test

The Problem: Members of the Town of Colonie Golfers' Loop frequently raise concerns to Mr. Lange, as its leader, about how the league is run. The most frequent concern raised is that the teams competing each week are not statistically even. In other words, members raise concerns that one or more teams have a statistical advantage over other teams. To evaluate the validity of these claims, Mr. Lange has decided to use a mix of statistical hypothesis tests discussed in this course to evaluate the teams from Outing #14 in calendar-year 2016 (2016, #14). One is the Equal Vari- ances F Test, one is Welch's T Test, and the other is the 2-Sample T Test

MATLAB: An Introduction with Applications
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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The Problem: Members of the Town of Colonie Golfers' Loop frequently raise concerns to Mr. Lange, as its leader, about how the league is run. The most frequent concern raised is that the teams competing each week are not statistically even. In other words, members raise concerns that one or more teams have a statistical advantage over other teams. To evaluate the validity of these claims, Mr. Lange has decided to use a mix of statistical hypothesis tests discussed in this course to evaluate the teams from Outing #14 in calendar-year 2016 (2016, #14). One is the Equal Vari- ances F Test, one is Welch's T Test, and the other is the 2-Sample T Test for Equal Means. In this particular outing, seven teams were competing for the win. A random sample of eight prior scores from each team member was collected, and the summary statistics are shown below (correct to three decimal places). Team Sample Size Sample Mean | Sample Variance 1 24 2 32 3 32 4 5 6 7 32 32 32 32 76.500 79.656 79.500 82.375 80.406 80.281 80.438 To test for statistical evenness among these teams using the mix of tests we described above, however, we will have to adjust the significance levels we are accustomed to using. Use the table on the next page to help you: If you are using...... use 0.238% 5% 1% 0.048% 0.1% 0.005% 14.522 18.233 13.097 47.984 18.314 11.047 14.383 1
Transcribed Image Text:The Problem: Members of the Town of Colonie Golfers' Loop frequently raise concerns to Mr. Lange, as its leader, about how the league is run. The most frequent concern raised is that the teams competing each week are not statistically even. In other words, members raise concerns that one or more teams have a statistical advantage over other teams. To evaluate the validity of these claims, Mr. Lange has decided to use a mix of statistical hypothesis tests discussed in this course to evaluate the teams from Outing #14 in calendar-year 2016 (2016, #14). One is the Equal Vari- ances F Test, one is Welch's T Test, and the other is the 2-Sample T Test for Equal Means. In this particular outing, seven teams were competing for the win. A random sample of eight prior scores from each team member was collected, and the summary statistics are shown below (correct to three decimal places). Team Sample Size Sample Mean | Sample Variance 1 24 2 32 3 32 4 5 6 7 32 32 32 32 76.500 79.656 79.500 82.375 80.406 80.281 80.438 To test for statistical evenness among these teams using the mix of tests we described above, however, we will have to adjust the significance levels we are accustomed to using. Use the table on the next page to help you: If you are using...... use 0.238% 5% 1% 0.048% 0.1% 0.005% 14.522 18.233 13.097 47.984 18.314 11.047 14.383 1
1. For each pair of teams, do all of the following: (a) Compute the f* statistic for the Equal Variances F Test and determine the numerator and denominator degrees of freedom on the F distribution. Make sure to have f* ≥ 1. (b) Compute ao for the Equal Variances F Test, as discussed in class. Can we conclude that the two teams' population variances differ? (c) Using your answer to (b), are we allowed to use the 2-Sample T Test for Equal Means to determine whether the two teams are statistically even? Or must we use Welch's T Test? (d) Compute the t* test statistic for the T test chosen in (c). Also compute the degrees of freedom on the T distribution needed for the chosen test Compute ao for the chosen T test. Can we conclude that the two teams are not statistically even?
Transcribed Image Text:1. For each pair of teams, do all of the following: (a) Compute the f* statistic for the Equal Variances F Test and determine the numerator and denominator degrees of freedom on the F distribution. Make sure to have f* ≥ 1. (b) Compute ao for the Equal Variances F Test, as discussed in class. Can we conclude that the two teams' population variances differ? (c) Using your answer to (b), are we allowed to use the 2-Sample T Test for Equal Means to determine whether the two teams are statistically even? Or must we use Welch's T Test? (d) Compute the t* test statistic for the T test chosen in (c). Also compute the degrees of freedom on the T distribution needed for the chosen test Compute ao for the chosen T test. Can we conclude that the two teams are not statistically even?
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