In a recent survey of 600 adults,16.4% indicated that they had fallen asleep in front of the television in the past month.Which of the following intervals represents a 98% confidence interval for the population proportion?
A)0.137 to 0.192
B)0.140 to 0.189
C)0.129 to 0.199
D)0.143 to 0.186

Question

Quizplus · Accepted Answer

To calculate a 98% confidence interval for the population proportion, we use the formula: $$ \hat{p} \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} $$ where $\hat{p}$ is the sample proportion, $Z_{\alpha/2}$ is the Z-score corresponding to the confidence level (for 98%, it's approximately 2.33), and $n$ is the sample size. Given $\hat{p} = 0.164$ and $n = 600$, the calculation yields an interval approximately from 0.129 to 0.199, which matches option C.

In a Recent Survey of 600 Adults,16