Question

determine the point estimate of the population mean and margin of error for the confidence interval lower bound is 19, upper bound is 23 the point estimate of the population mean is 21 the margin of error for the confidence interval is

Explanation:

Step1: Calculate the point estimate of the population mean

The formula for the point estimate of the population mean \(\mu\) (when given a confidence interval \((L, U)\) where \(L\) is the lower bound and \(U\) is the upper bound) is \(\bar{x}=\frac{L + U}{2}\). Substituting \(L = 19\) and \(U=23\), we get \(\bar{x}=\frac{19 + 23}{2}=\frac{42}{2}=21\).

Step2: Calculate the margin of error

The formula for the margin of error \(E\) is \(E=\frac{U - L}{2}\). Substituting \(L = 19\) and \(U = 23\), we have \(E=\frac{23-19}{2}=\frac{4}{2}=2\).

Answer:

The point estimate of the population mean is \(21\). The margin of error for the confidence interval is \(2\).