Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS e-mail for non-business communications.A random sample of 200 e-mail messages was selected.Thirty of the messages were not business related.The 90% confidence interval for the population proportion is _________.
A)0.108 to 0.192
B)0.153 to 0.247
C)0.091 to 0.209
D)0.145 to 0.255
E)0.255 to 0.265

Question

Quizplus · Accepted Answer

The proportion of non-business related emails is 30/200 = 0.15. To calculate the 90% confidence interval for the population proportion, we use the formula for the confidence interval of a proportion: $p \pm z\sqrt{\frac{p(1-p)}{n}}$, where $p$ is the sample proportion, $z$ is the z-score corresponding to the confidence level (for 90%, $z$ is approximately 1.645), and $n$ is the sample size. Plugging in the values, we get $0.15 \pm 1.645\sqrt{\frac{0.15(0.85)}{200}}$, which calculates to an interval of approximately $0.108$ to $0.192$, making option A correct.