The number of successes and the sample size are given for a simple random sample from a population. Use theone-proportion z-interval procedure to find the required confidence interval.
-$$\mathrm { n } = 85 , \mathrm { x } = 41 ; 98 \% \text { level }$$
A)$0.375$ to $0.589$
B) $0.376$ to $0.588$
C) $0.355$ to $0.609$
D) $0.356$ to $0.608$

Question

The number of successes and the sample size are given for a simple random sample from a population. Use theone-proportion z-interval procedure to find the required confidence interval.
-$$\mathrm { n } = 85 , \mathrm { x } = 41 ; 98 \% \text { level }$$  
A)$0.375$ to $0.589$
B) $0.376$ to $0.588$
C) $0.355$ to $0.609$
D) $0.356$ to $0.608$

Quizplus · Accepted Answer

The sample proportion $\hat{p} = \frac{x}{n} = \frac{41}{85}$. For a 98% confidence interval, the z-value is approximately 2.33. Using the formula for the confidence interval $\hat{p} \pm z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$, the interval is calculated to be approximately 0.356 to 0.608.

The Number of Successes and the Sample Size Are Given n=85,x=41;98% level \mathrm { n } = 85 , \mathrm { x } = 41 ; 98 \% \text { level }n=85,x=41;98% level

The Number of Successes and the Sample Size Are Given $\mathrm { n } = 85 , \mathrm { x } = 41 ; 98 \% \text { level }$