Question

in a survey of 2480 golfers, 15% said they were left - handed. the surveys margin of error was 3%. construct a confidence interval for the proportion of left - handed golfers.
a. (0.12,0.18)
b. (0.11,0.19)
c. (0.12,0.15)
d. (0.18,0.21)

Explanation:

Step1: Calculate the lower bound

The formula for the lower bound of a confidence interval for a proportion is \(\hat{p}-E\), where \(\hat{p}\) is the sample proportion and \(E\) is the margin of error. Given \(\hat{p} = 0.15\) and \(E=0.03\), the lower bound is \(0.15 - 0.03\).
\(0.15-0.03=0.12\)

Step2: Calculate the upper bound

The formula for the upper bound of a confidence interval for a proportion is \(\hat{p}+E\). Using \(\hat{p} = 0.15\) and \(E = 0.03\), the upper bound is \(0.15+0.03\).
\(0.15 + 0.03=0.18\)

Answer:

A. \((0.12,0.18)\)