What is the approximate width of a 90 percent confidence interval for the true population proportion if there are 12 successes in a sample of 25?
A)± .196
B)± .164
C)± .480
D)± .206

Question

Quizplus · Accepted Answer

First, we need to find the sample proportion: 
p-hat = 12/25 = 0.48 
Next, we can use the formula for the margin of error for a proportion: 
ME = z*sqrt((p-hat*(1-p-hat))/n) 
where z is the critical value for the desired confidence level (in this case, 90% confidence corresponds to a z-value of 1.645), p-hat is the sample proportion, and n is the sample size.
ME = 1.645*sqrt((0.48*(1-0.48))/25) = 0.082 
Finally, we can construct the confidence interval: 
CI = p-hat ± ME = 0.48 ± 0.082 = [0.398, 0.562] 
The width of this interval is approximately 0.164, which is answer choice B.

What Is the Approximate Width of a 90 Percent Confidence