Question

determine the point estimate of the population mean and margin of error for the confidence interval lower bound is 20, upper bound is 24. the point estimate of the population mean is. the margin of error for the confidence interval is.

Explanation:

Step1: Calculate the point estimate of the population mean

The point estimate of the population mean (\(\mu\)) for a confidence interval is the mid - point of the interval. The formula for the mid - point is \(\bar{x}=\frac{\text{Lower bound}+\text{Upper bound}}{2}\).
Substitute the lower bound \(L = 20\) and upper bound \(U = 24\) into the formula: \(\bar{x}=\frac{20 + 24}{2}=\frac{44}{2}=22\).

Step2: Calculate the margin of error

The margin of error (\(E\)) is given by the formula \(E=\frac{\text{Upper bound}-\text{Lower bound}}{2}\).
Substitute \(L = 20\) and \(U = 24\) into the formula: \(E=\frac{24 - 20}{2}=\frac{4}{2}=2\).

Answer:

The point estimate of the population mean is \(22\).
The margin of error for the confidence interval is \(2\).