A large national company is considering negotiating cellular phone rates for its employees.The Human Resource department would like to estimate the proportion of its employee population who own an Apple iPhone.A random sample of size 250 is taken and 40% of the sample own and iPhone.The 90% confidence interval to estimate the population proportion is ____.
A)0.35 to 0.45
B)0.34 to 0.46
C)0.38 to 0.42
D)0.39 to 0.41
E)0.40 to 0.45

Question

Quizplus · Accepted Answer

The 90% confidence interval for a proportion is calculated using the formula: $$CI = \hat{p} \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$ where $\hat{p}$ is the sample proportion (0.40), $n$ is the sample size (250), and $Z_{\alpha/2}$ is the Z-score corresponding to the desired confidence level (for 90% confidence, $Z_{\alpha/2} \approx 1.645$). Plugging in the values: $$CI = 0.40 \pm 1.645 \sqrt{\frac{0.40(0.60)}{250}}$$ This calculation results in a confidence interval of approximately 0.35 to 0.45, making option A correct.

A Large National Company Is Considering Negotiating Cellular Phone Rates