Question

Use the given data to find the 95% confidence interval estimate of the population mean μμ. Assume that the population has a normal distribution.

IQ scores of professional athletes:
Sample size n=10n=10
Mean x⎯⎯⎯=103x¯=103
Standard deviation s=10s=10
<μ<<μ

Answer 1

To find the 95% confidence interval estimate of the population mean, use the formula (x - z * (s / √n), x + z * (s / √n)), where x is the sample mean, s is the standard deviation, n is the sample size, and z is the z-score corresponding to the desired confidence level.

Step-by-step explanation:

To find the 95% confidence interval estimate of the population mean, we can use the formula:

(x - z * (s / √n), x + z * (s / √n))

Where x is the sample mean, s is the standard deviation, n is the sample size, and z is the z-score corresponding to the desired confidence level.

In this case, the sample mean is 103, the standard deviation is 10, and the sample size is 10.

Using a z-score of 1.96 for a 95% confidence level, we can calculate:

(103 - 1.96 * (10 / √10), 103 + 1.96 * (10 / √10))

= (95.17, 110.83)

So, the 95% confidence interval estimate for the population mean µ is (95.17, 110.83).