Question

Salaries of 38 college graduates who took a statistics course in college have a​ mean,x, of $ 64,600. Assuming a standard​deviation, sigma, of ​$12,689, construct a 99​% confidence interval for estimating the population mean u.

Answer 1

To construct a 99% confidence interval for estimating the population mean, use the formula Confidence interval = x ± Z * (σ / √n), where x is the sample mean, Z is the Z-score corresponding to the desired confidence level, σ is the standard deviation, and n is the sample size.

Step-by-step explanation:

To construct a 99% confidence interval for estimating the population mean (μ), we will use the formula:

Confidence interval = x ± Z * (σ / √n)

where x is the sample mean, Z is the Z-score corresponding to the desired confidence level, σ is the standard deviation, and n is the sample size.

Using the given information:

• x = $64,600
• σ = $12,689
• Z-value for a 99% confidence level is approximately 2.57 (obtained from the Z-table)

Plugging these values into the formula:

Confidence interval = $64,600 ± 2.57 * ($12,689 / √38) = $64,600 ± $5,170.08

The 99% confidence interval for estimating the population mean is approximately $59,429.92 to $69,770.08.