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 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?
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The point estimate of a proportion is always the midpoint of its confidence interval.
Updated On: Jul 4, 2026
- 0.16
- 0.241
- 0.401
- 0.561
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The Correct Option is C
Solution and Explanation
Step 1: A confidence interval for a proportion is always constructed symmetrically around the point estimate \(\hat{p}\), running from \(\hat{p} - E\) to \(\hat{p} + E\), where \(E\) is the margin of error.
Step 2: Because the interval is symmetric, the point estimate \(\hat{p}\) is simply the midpoint of the given interval.
\[ \hat{p} = \frac{0.241 + 0.561}{2} = \frac{0.802}{2} = 0.401 \]Step 2: Because the interval is symmetric, the point estimate \(\hat{p}\) is simply the midpoint of the given interval.
Step 3: So the best point estimate of the true proportion of employees preferring plan A is \(0.401\).
The correct answer is (C) 0.401.
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