Use the given data to construct a confidence interval of the requested level.
x=114, n=228 , confidence level 90%
A) (0.446,0.554)
B) (0.410,0.590)
C) (0.467,0.533)
D) (0.458,0.542)

Question

Use the given data to construct a confidence interval of the requested level.
 x=114, n=228 , confidence level  90% 
A)  (0.446,0.554) 
B)  (0.410,0.590) 
C)  (0.467,0.533) 
D)  (0.458,0.542)

Quizplus · Accepted Answer

The confidence interval for a proportion is calculated using the formula $p \pm Z \sqrt{\frac{p(1-p)}{n}}$, where $p = \frac{x}{n}$, $Z$ is the Z-score corresponding to the confidence level, $n$ is the sample size, and $x$ is the number of successes. For a 90% confidence level, the Z-score is approximately 1.645. Here, $p = \frac{114}{228} = 0.5$. Plugging these values into the formula gives the interval (0.446, 0.554).

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