Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. $n = 195 , x = 162 ; 95 \%$ confidence
A) $0.778

Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. $n = 195 , x = 162 ; 95 \%$ confidence
A) $0.778 < p < 0.883$
B) $0.788 < p < 0.873$
C) $0.789 < p < 0.873$
D) $0.777 < p < 0.884$

Quizplus · Accepted Answer

The sample proportion is $\hat{p} = x/n = 162/195 = 0.831$. For a 95% confidence level, the critical value is $z^* = 1.96$. The margin of error is $E = z^* \sqrt{\hat{p}(1-\hat{p})/n} = 1.96 \sqrt{0.831(1-0.831)/195} = 0.053$. Therefore, the confidence interval is $0.831 \pm 0.053 = (0.778, 0.883)$.

Use the Given Degree of Confidence and Sample Data to Construct