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ECON 230 Lab 7: Chi-Squared Testing and Independence of Slugging Percentage and Salary, Lab Reports of Statistics

Loyola Marymount University (LMU)Statistics

In this lab, students learn about chi-squared testing and apply it to determine if there is a significant relationship between slugging percentage and salary for 40 players. The lab involves calculating means, classifying observations into categories, and testing the hypothesis of independence using a chi-square test. Students are expected to hand in an answer sheet with their results.

Typology: Lab Reports

Pre 2010

Uploaded on 08/18/2009

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ECON 230
Lab 7
The goal of this lab is to learn about chi-squared testing (This lab is out of 12 points).
For this lab you will use chi-square testing to see if there is a significant relationship between
slugging percentage (your V2) and salary (your V3) for your 40 players.
MAKE SURE TO HAND IN THE ANSWER SHEET ONLY WHEN YOU HAND IN LAB 7!
(2 points) 1. Use Excel to find the mean of your players’ slugging percentages and the mean of your
players’ salaries. Classify each of your 40 observations as falling into one of the
following four categories.
1. Value of slugging percentage is less than or equal to the mean and value of salary is
less than or equal to the mean.
(slugging percentage low, salary low)
2. Value of slugging percentage is less than or equal to the mean, but value of salary is
greater than the mean.
(slugging percentage low, salary high)
3. Value of slugging percentage is greater than the mean, but value of salary is less than
or equal to the mean.
(slugging percentage high, salary low)
4. Value of slugging percentage is greater than the mean and value of salary is greater
than the mean.
(slugging percentage high, salary high)
Enter into the table the frequencies of each of these categories in your data. The four
numbers that you enter in the table should add up to 40.
On the next page, there is an example of how you need to classify your observations for
this problem.
(2 points) 2. If slugging percentage and salary are independent, then we would expect that salary is
equally likely to be high, regardless of whether slugging percentage is high or low.
Given the sums of the two rows and two columns that you found in problem 1, what
would you expect the table to look like if slugging percentage and salary are
independent? Round your answers to the nearest tenth.
(Hint: If slugging percentage and salary are independent, then the probability of salary
being low (or high) does not depend on whether slugging percentage is low or high. So
the fraction of the observations in column 1 that are in row 1 should be the same as the
fraction of observations in column 2 that are in row 1.)
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Lab 7 The goal of this lab is to learn about chi-squared testing (This lab is out of 12 points)****. For this lab you will use chi-square testing to see if there is a significant relationship between slugging percentage (your V 2 ) and salary (your V 3 ) for your 40 players. MAKE SURE TO HAND IN THE ANSWER SHEET ONLY WHEN YOU HAND IN LAB 7! ( 2 points) 1. Use Excel to find the mean of your players’ slugging percentages and the mean of your players’ salaries. Classify each of your 40 observations as falling into one of the following four categories.

  1. Value of slugging percentage is less than or equal to the mean and value of salary is less than or equal to the mean. (slugging percentage low, salary low)
  2. Value of slugging percentage is less than or equal to the mean, but value of salary is greater than the mean. (slugging percentage low, salary high)
  3. Value of slugging percentage is greater than the mean, but value of salary is less than or equal to the mean. (slugging percentage high, salary low)
  4. Value of slugging percentage is greater than the mean and value of salary is greater than the mean. (slugging percentage high, salary high) Enter into the table the frequencies of each of these categories in your data. The four numbers that you enter in the table should add up to 40. On the next page, there is an example of how you need to classify your observations for this problem. ( 2 points) 2. If slugging percentage and salary are independent, then we would expect that salary is equally likely to be high, regardless of whether slugging percentage is high or low. Given the sums of the two rows and two columns that you found in problem 1, what would you expect the table to look like if slugging percentage and salary are independent? Round your answers to the nearest tenth. (Hint: If slugging percentage and salary are independent, then the probability of salary being low (or high) does not depend on whether slugging percentage is low or high. So the fraction of the observations in column 1 that are in row 1 should be the same as the fraction of observations in column 2 that are in row 1.)

Lab 7 ( 6 points) 3. Using the tables from problems 1. and 2. , test at the 5% significance level the hypothesis that slugging percentage and salary are independent. Your null hypothesis is that they are independent and the alternative hypothesis is that they are dependent. i) The test statistic 2 2 (^ O^ E ) E

 follows a chi-square distribution with how many

degrees of freedom? ii) What is the value of the test statistic? iii) What is the critical value for this test? iv) Do you reject the hypothesis that slugging percentage and salary are independent at the 5% significance level? ( 2 points) 4. In two sentences, describe at least two things you’ve learned by analyzing your data this semester. Example for problem 1: Suppose that my mean slugging percentage was 0.425 and my mean salary was $1,500,000. Then suppose the table below describes slugging percentage and salary for three players: Cirillo, Jeff IF 0.293 6975000 Davis, Ben C 0.4 1400000 Estrada, Johnny C 0.45 312500 Each of these players goes into the following categories. Slugging percentage low Slugging percentage high Total Salary low Ben Davis Johnny Estrada Salary high Jeff Cirillo Total For example, Jeff Cirillo goes into the lower-left box because his slugging percentage (0.293) is below the mean and his salary ($6,975,000) is above the mean. You need to classify each of your forty players by comparing their slugging percentages and salaries to the means for each variable. Be careful to make sure to you use your mean for slugging percentage and your mean for salary, and not the numbers used in this example.

Lab 7 iii) Critical value = _____________________ iv) Circle one: Accept H 0 Reject H 0 4.