John Calipari, head basketball coach for the 2012 national champion University of Kentucky Wildcats, is the highest paid coach in college basketball with an annual salary of $5.4 million (USA Today, March 29, 2012). The sample below shows the head basketball coach's salary for a sample of 10 schools playing NCAA Division 1 basketball. Salary data are in millions of dollars. University Coach's Salary University Coach's Salary Indiana 2.2 Syracuse 1.5 Xavier .5 Murray State .2 Texas 2.4 Florida State 1.5 Connecticut 2.7 South Dakota State .1 West Virginia 2.0 Vermont .2 a. Use the sample mean for the 10 schools to estimate the population mean annual salary for head basketball coaches at colleges and universities playing NCAA Division 1 basketball (to 2 decimals). 1.33 b. Use the data to estimate the population standard deviation for the annual salary for head basketball coaches (to 4 decimals). c. What is the 95% confidence interval for the population variance (to 2 decimals)?
John Calipari, head basketball coach for the 2012 national champion University of Kentucky Wildcats, is the highest paid coach in college basketball with an annual salary of $5.4 million (USA Today, March 29, 2012). The sample below shows the head basketball coach's salary for a sample of 10 schools playing NCAA Division 1 basketball. Salary data are in millions of dollars. University Coach's Salary University Coach's Salary Indiana 2.2 Syracuse 1.5 Xavier .5 Murray State .2 Texas 2.4 Florida State 1.5 Connecticut 2.7 South Dakota State .1 West Virginia 2.0 Vermont .2 a. Use the sample mean for the 10 schools to estimate the population mean annual salary for head basketball coaches at colleges and universities playing NCAA Division 1 basketball (to 2 decimals). 1.33 b. Use the data to estimate the population standard deviation for the annual salary for head basketball coaches (to 4 decimals). c. What is the 95% confidence interval for the population variance (to 2 decimals)?
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
Transcribed Image Text:**Educational Transcript on Coaching Salaries in NCAA Division 1 Basketball**
John Calipari, head basketball coach for the 2012 national champion University of Kentucky Wildcats, is cited as the highest paid coach in college basketball with an annual salary of $5.4 million (USA Today, March 29, 2012). Below is a sample showing the head basketball coach's salary for 10 schools participating in NCAA Division 1 basketball. These figures are in millions of dollars.
| University | Coach’s Salary |
|-----------------|----------------|
| Indiana | 2.2 |
| Xavier | 0.5 |
| Texas | 2.4 |
| Connecticut | 2.7 |
| West Virginia | 2.0 |
| Syracuse | 1.5 |
| Murray State | 0.2 |
| Florida State | 1.5 |
| South Dakota State | 0.1 |
| Vermont | 0.2 |
**Statistical Analysis**
a. **Sample Mean Calculation**: Use the sample mean from the 10 schools to estimate the population mean annual salary for head basketball coaches at colleges participating in NCAA Division 1 basketball. The sample mean is calculated to be 1.33 million dollars.
b. **Population Standard Deviation Estimation**: An attempt was made to use the data to estimate the population standard deviation for the annual salary of head basketball coaches, to four decimal places.
c. **95% Confidence Interval for Population Variance**: The confidence interval is provided as (0.48, 3.35).
d. **95% Confidence Interval for Population Standard Deviation**: The confidence interval is given as (0.69, 1.83).
These calculations allow for data-driven estimates about the financial distributions of head coach salaries in basketball programs across different universities.
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