What is the approximate width of an 80 percent confidence interval for the true population proportion if there are 12 successes in a sample of 80?
A)± .078
B)± .066
C)± .051
D)± .094

Question

Quizplus · Accepted Answer

To find the width of the 80% confidence, we need to find the margin of error first. 
Margin of Error = Critical Value * Standard Error
The critical value for an 80% confidence interval is 1.28 (using a table or calculator).
The standard error = sqrt[(p-hat*(1-p-hat))/n]
Here, p-hat = 12/80 = 0.15
So, Standard Error = sqrt[(0.15*(1-0.15))/80] = 0.0432
Now, Margin of error = 1.28 * 0.0432 = 0.05530
So, the approximate width of the 80% confidence interval = 2 * Margin of Error = ± 0.1106, which is approximately equal to ± 0.051.
Therefore, the answer is C.

What Is the Approximate Width of an 80 Percent Confidence