Final answer:
To find the 95% confidence interval estimate of the population mean μ for IQ scores of professional athletes, use the formula (x - EBM, x + EBM), where x is the sample mean and EBM is the error bound for the population mean. For a sample size of 10, a sample mean of 105, and a standard deviation of 13, the 95% confidence interval estimate is (96.84, 113.16).
Step-by-step explanation:
To calculate the 95% confidence interval estimate of the population mean μ, we use the formula:
(x - EBM, x + EBM)
Where x is the sample mean and EBM is the error bound for the population mean.
Given that the sample size (n) is 10, the sample mean (x) is 105, and the standard deviation is 13, we can calculate the error bound using the formula:
EBM = (Z * σ) / √n
Where Z is the z-score corresponding to the desired confidence level. For a 95% confidence level, Z is approximately 1.96.
Substituting the values into the formula, we get:
EBM = (1.96 * 13) / √10
Simplifying the equation, we find the error bound is approximately 8.16.
Therefore, the 95% confidence interval estimate for the population mean μ is (105 - 8.16, 105 + 8.16), or (96.84, 113.16).