Question

A random sample of professional wrestlers was obtained, and the annual salary (in dollars) for each was recorded. The summary statistics were ×547,500 and n5 18. Assume the distribution of annual salary is normal with s 58,500 .

a. Find a 90% confidence interval for the true mean annual salary for all professional wrestlers.
b. How large a sample is necessary for the bound on the error of estimation to be 3000 ?
c. How large a sample is necessary for the bound on the error of estimation to be 1000?

Answer 1

The question is about determining confidence intervals and necessary sample sizes based on standard deviation, sample mean, and desired precision in the context of professional wrestlers' salaries.

Step-by-step explanation:

The question involves creating confidence intervals and determining sample sizes, which are fundamental concepts in statistics. Specifically, it is about professional wrestlers' salaries and the degree of certainty we can have about the average salary based on a sample.

To find a 90% confidence interval for the true mean annual salary, we use the sample mean ($547,500), the standard deviation ($8,500), and the sample size (18). Using the t-distribution with 17 degrees of freedom (n-1), we find the critical t-value and then calculate the margin of error. The interval is then the sample mean plus or minus this margin.

To find the necessary sample size to achieve a specific error bound, we use the formula for the margin of error which involves the standard deviation, z-score of the confidence level, and the desired bound on the error (E). We solve for the sample size (n) to keep the margin of error within $3,000 and $1,000 for the respective parts of the question.