Refer to the Baseball 2012 data, which report information on the 30 Major League
ID: 3128226 • Letter: R
Question
Refer to the Baseball 2012 data, which report information on the 30 Major League Baseball teams for the 2012 season. a. Conduct a test of hypothesis to determine whether the mean salary of the teams was different from $80.0 million. Use the .05 significance level. b. Using a 5% significance level, conduct a test of hypothesis to determine whether the mean attendance was more than 2,000,000 per team.
Team Salary 2012 Attendance X1 X5 X7 Arizona Diamondbacks 74.3 2.18 Atlanta Braves 83.3 2.42 Baltimore Orioles 81.4 2.1 Boston Red Sox 173.2 3.04 Chicago Cubs 88.2 2.88 Chicago White Sox 96.9 1.97 Cincinnati Reds 82.2 2.35 Cleveland Indians 78.4 1.6 Colorado Rockies 78.1 2.63 Detroit Tigers 132.3 3.03 Houston Astros 60.7 1.61 Kansas City Royals 60.9 1.74 Los Angeles Angels 154.5 3.06 Los Angeles Dodgers 95.1 3.32 Miami Marlins 118.1 2.22 Milwaukee Brewers 97.7 2.83 Minnesota Twins 94.1 2.78 New York Mets 93.4 2.24 New York Yankees 198 3.54 Oakland Athletics 55.4 1.68 Philadelphia Phillies 174.5 3.57 Pittsburgh Pirates 63.4 2.09 San Diego Padres 55.2 2.12 San Francisco Giants 117.6 3.38 Seattle Mariners 82 1.72 St. Louis Cardinals 110.3 3.26 Tampa Bay Rays 64.2 1.56 Texas Rangers 120.5 3.46 Toronto Blue Jays 75.5 2.1 Washington Nationals 81.3 2.37Explanation / Answer
Refer to the Baseball 2012 data, which report information on the 30 Major League Baseball teams for the 2012 season. a. Conduct a test of hypothesis to determine whether the mean salary of the teams was different from $80.0 million. Use the .05 significance level.
Two tailed test
t Test for Hypothesis of the Mean
Data
Null Hypothesis m=
80
Level of Significance
0.05
Sample Size
30
Sample Mean
98.0233
Sample Standard Deviation
36.8323
Intermediate Calculations
Standard Error of the Mean
6.7246
Degrees of Freedom
29
t Test Statistic
2.6802
Two-Tail Test
Lower Critical Value
-2.0452
Upper Critical Value
2.0452
p-Value
0.0120
Reject the null hypothesis
Calculated t =2.6802 falls in the rejection region. The null hypothesis is rejected.
We conclude that mean salary of the teams was different from $80.0 million.
b. Using a 5% significance level, conduct a test of hypothesis to determine whether the mean attendance was more than 2,000,000 per team.
Upper tail test.
t Test for Hypothesis of the Mean
Data
Null Hypothesis m=
2
Level of Significance
0.05
Sample Size
30
Sample Mean
2.495
Sample Standard Deviation
0.6421
Intermediate Calculations
Standard Error of the Mean
0.1172
Degrees of Freedom
29
t Test Statistic
4.2221
Upper-Tail Test
Upper Critical Value
1.6991
p-Value
0.0001
Reject the null hypothesis
Calculated t =4.2221 falls in the rejection region.
The null hypothesis is rejected.
We conclude that mean attendance was more than 2,000,000 per team.
t Test for Hypothesis of the Mean
Data
Null Hypothesis m=
80
Level of Significance
0.05
Sample Size
30
Sample Mean
98.0233
Sample Standard Deviation
36.8323
Intermediate Calculations
Standard Error of the Mean
6.7246
Degrees of Freedom
29
t Test Statistic
2.6802
Two-Tail Test
Lower Critical Value
-2.0452
Upper Critical Value
2.0452
p-Value
0.0120
Reject the null hypothesis