Question

Salaries of 42 college graduates who took a statistics course in college have a mean, x, of $64,100.

Assuming a standard deviation, sigma, of $10,016, construct a 99% confidence interval for estimating the population mean μ
(Round to the nearest integer as needed.)

Answer 1

To construct a 99% confidence interval for estimating the population mean μ, you can use the formula: CI = x ± Z * (σ/√n), where x is the sample mean, Z is the critical value, σ is the standard deviation, and n is the sample size. Plugging in the values given, the 99% confidence interval for estimating the population mean μ is approximately $60,474 to $67,726.

Step-by-step explanation:

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

CI = x ± Z * (σ/√n)

Where x is the sample mean ($64,100), Z is the critical value for a 99% confidence level (2.58), σ is the standard deviation ($10,016), and n is the sample size (42).

Plugging in the values, we get: CI = $64,100 ± 2.58 * ($10,016/√42)

Simplifying further, the confidence interval becomes: CI ≈ $64,100 ± $3,626

Rounding to the nearest integer, the 99% confidence interval for estimating the population mean μ is approximately $60,474 to $67,726.