Question

A random sample of 40 students has a mean annual earnings of $3,120, and assume that the population standard deviation is $677. Construct the confidence interval for the population mean, μ, if c equals 0.95.

Answer 1

To construct the confidence interval, use the formula CI = Xbar ± Z * (σ / sqrt(n)). Given Xbar = $3,120, σ = $677, n = 40, and a 0.95 confidence level, the confidence interval for the population mean μ is approximately $2,863.58 to $3,376.42.

Step-by-step explanation:

To construct the confidence interval for the population mean, we can use the formula:

CI = Xbar ± Z * (σ / sqrt(n))

Where Xbar is the sample mean, Z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

1. Given Xbar = $3,120, σ = $677, n = 40, and the desired confidence level is 0.95.
2. First, find the z-score for a 0.95 confidence level, which corresponds to 1.96.
3. Plug in the values into the formula:
4. CI = $3,120 ± 1.96 * ($677 / sqrt(40))
5. Simplify the formula to find the confidence interval.

The confidence interval for the population mean μ, with a 0.95 confidence level, is approximately $2,863.58 to $3,376.42