Question

A marketing research company needs to estimate which of two medical plans its employees prefer. A random sample of \(n\) employees produced the following 98% confidence interval for the proportion of employees who prefer plan A: \((0.241, 0.561)\). What is a good point estimate for estimating the true proportion of employees who prefer that plan?

• A. 0.16
• B. 0.241
• C. 0.401
• D. 0.561

Hint:

The point estimate of a proportion is always the midpoint of its confidence interval.

Answer 1

The Correct Option is C

Step 1: The margin of error $E$ is half the total width of the confidence interval.

\[ E = \frac{0.561 - 0.241}{2} = \frac{0.320}{2} = 0.16 \]

Step 2: The point estimate $\hat{p}$ can be recovered by subtracting the margin of error from the upper limit, or equivalently adding it to the lower limit.

\[ \hat{p} = 0.561 - 0.16 = 0.401 \]

Step 3: Checking with the lower limit: $0.241 + 0.16 = 0.401$, the same value, which confirms the estimate.

\[ \boxed{\hat{p} = 0.401} \]