A financial analyst is interested in estimating the proportion of publicly traded companies on the Toronto Stock Exchange that have cash balances of more than 10 percent of the total assets of the company. A random sample of 100 companies shows that 13 had cash balances of more than 10 percent of assets. The 90 % confidence interval estimate is
A) 0.0747 to 0.1853.
B) 0.0641 to 0.1959.
C) -0.0870 to 0.1730.
D) -0.0507 to 0.1494.
E) -0.0412 to 0.1588.

Question

Quizplus · Accepted Answer

The correct 90% confidence interval for the proportion is calculated using the formula for a confidence interval for a proportion: $\hat{p} \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$, where $\hat{p} = \frac{13}{100} = 0.13$, $n = 100$, and $Z_{\alpha/2}$ for a 90% confidence level is approximately 1.645. Plugging these values into the formula gives the interval $0.13 \pm 1.645 \sqrt{\frac{0.13(1-0.13)}{100}}$, which calculates to approximately $0.0747$ to $0.1853$.

A Financial Analyst Is Interested in Estimating the Proportion of Publicly