Use the given data to construct a confidence interval of the requested level. x = 78, n = 124, confidence level 98%
A) (0.586, 0.672)
B) (0.394, 0.864)
C) (0.544, 0.714)
D) (0.528, 0.730)

Question

Quizplus · Accepted Answer

The formula for calculating the confidence interval for population proportion is:
$\hat{p} \pm z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$
where $\hat{p} = \frac{x}{n}$ is the sample proportion, $n$ is the sample size, and $z_{\alpha/2}$ is the z-score corresponding to the confidence level. 
Substituting the given values,
$\hat{p} = \frac{78}{124} = 0.629$
$z_{\alpha/2} = z_{0.01} = 2.33$
$n=124$
Plugging in these values, we get:
$0.629 \pm 2.33 \sqrt{\frac{0.629(1-0.629)}{124}}$
$\Rightarrow 0.629 \pm 0.101$
$\Rightarrow (0.528, 0.730)$
Hence, the answer is D.

Use the Given Data to Construct a Confidence Interval of the Requested