Exercise 3: Sample Distribution of the After a disappointing season, President A ntermural basketball team. His replaceme who is 6'4" tall. The average points per g irst thirty games. President Points Monroe 10 Madison 14 Jefferson Washington 20 30 Lincel 36

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**Exercise 3: Sample Distribution of the Sample Means**

After a disappointing season, President Adams, who is 5'7" tall, is voted off the Presidents' intramural basketball team. His replacement is a lanky newcomer, President Abraham Lincoln, who is 6'4" tall. The average points per game for the Presidents’ team after President Lincoln’s first thirty games are shown below:

| President  | Points |
|------------|--------|
| Monroe     | 10     |
| Madison    | 14     |
| Jefferson  | 20     |
| Washington | 30     |
| Lincoln    | 36     |

**Questions:**

A) Calculate the population mean, \(\mu\).

B) How many samples of two players from the five players are possible?

C) Calculate the samples means, show your results as a sampling distribution of sample means.

D) How many of the samples have sample error? Which ones, if any, do not?

E) Calculate the mean of the sampling distribution of sample means and compare it to the population mean.

F) Using the range, compare variability in the population to variability in the sampling distribution.

**Instructions:**
- Ensure calculations are clear and steps are methodical to help students understand the process of calculating means, sample distributions, and variability.
- Encourage students to consider the implications of sample error in data analysis and real-world contexts.
Transcribed Image Text:**Exercise 3: Sample Distribution of the Sample Means** After a disappointing season, President Adams, who is 5'7" tall, is voted off the Presidents' intramural basketball team. His replacement is a lanky newcomer, President Abraham Lincoln, who is 6'4" tall. The average points per game for the Presidents’ team after President Lincoln’s first thirty games are shown below: | President | Points | |------------|--------| | Monroe | 10 | | Madison | 14 | | Jefferson | 20 | | Washington | 30 | | Lincoln | 36 | **Questions:** A) Calculate the population mean, \(\mu\). B) How many samples of two players from the five players are possible? C) Calculate the samples means, show your results as a sampling distribution of sample means. D) How many of the samples have sample error? Which ones, if any, do not? E) Calculate the mean of the sampling distribution of sample means and compare it to the population mean. F) Using the range, compare variability in the population to variability in the sampling distribution. **Instructions:** - Ensure calculations are clear and steps are methodical to help students understand the process of calculating means, sample distributions, and variability. - Encourage students to consider the implications of sample error in data analysis and real-world contexts.
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