A decision maker is interested in estimating a population proportion. A sample of size n = 150 yields 115 successes. Based on these sample data, construct a 90% confidence interval estimate for the true population proportion.
A) (0.714, 0.826)
B) (0.717, 0.823)
C) (0.737, 0.803)
D) (0.750, 0.790)

Question

Quizplus · Accepted Answer

The sample proportion (p̂) is 115/150 = 0.77. For a 90% confidence interval, the z-value is approximately 1.645. The standard error (SE) is sqrt[(0.77)(0.23)/150] ≈ 0.035. The margin of error (ME) is 1.645 * SE ≈ 0.058. The confidence interval is p̂ ± ME, which is 0.77 ± 0.058, resulting in (0.712, 0.828). The closest option to these calculations is (0.714, 0.826).

A Decision Maker Is Interested in Estimating a Population Proportion