Question

Create your own single sample confidence interval problem for a large sample (greater than 30) and sports related. Provide the following information and describe the process to come to the answer (do not use this scenario or scenarios provided in the course material).

Scenario in a word problem (e.g., Want to know the CI for 17yr old high school football players and the number of calories they consume per day).
Number in the sample (e.g., 77 football players)
Sample mean (e.g., 3,500 calories)
Sample standard deviation (assume you know it, e.g., 300 calories)
Desired confidence interval (e.g. 90% CI)
Explain how you solved the problem and the resulting CI you came up with for the problem.

Answer 1

To construct a single sample confidence interval problem for a large sample and sports-related, consider the average distance that basketball players can shoot from the three-point line. Assume a sample of 100 basketball players, a sample mean of 21 feet, and a known sample standard deviation of 2 feet. The 95% confidence interval for the true mean distance is 19.572 to 22.428 feet.

Step-by-step explanation:

To create our own single sample confidence interval problem for a large sample and sports-related, let's consider the average distance that basketball players can shoot from the three-point line. Assume that a sample of 100 basketball players is surveyed. The sample mean is found to be 21 feet, and the sample standard deviation is known to be 2 feet. We want to construct a 95% confidence interval for the true mean distance that basketball players can shoot from the three-point line.

Solution:

The process to solve this problem is as follows:

1. Determine the sample size, which is 100 basketball players.
2. Calculate the sample mean, which is 21 feet.
3. Assume the population standard deviation is known to be 2 feet.
4. Find the critical value for a 95% confidence interval; for a large sample, this is approximately 1.96.
5. Calculate the standard error, which is the population standard deviation divided by the square root of the sample size: 2 / √100 = 0.2.
6. Construct the confidence interval by subtracting and adding the margin of error from the sample mean: 21 - 1.96(0.2) to 21 + 1.96(0.2) = 19.572 to 22.428.

Therefore, the 95% confidence interval for the true mean distance that basketball players can shoot from the three-point line is 19.572 to 22.428 feet.