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)± 0.078
B)± 0.066
C)± 0.051
D)± 0.094

Question

Quizplus · Accepted Answer

To find the approximate width of an 80 percent confidence interval, we first need to find the standard error(SE) of the sample proportion.

SE = sqrt(p_hat*q_hat/n)

where

p_hat = number of successes/total sample size
q_hat = 1 - p_hat
n = total sample size

p_hat = 12/80 = 0.15
q_hat = 1 - 0.15 = 0.85
n = 80

SE = sqrt(0.15*0.85/80) = 0.051

Now, to find the approximate width of the confidence interval, we can use the margin of error formula:

ME = z*SE

where

z = z-score for the desired level of confidence

For an 80% confidence interval, the z-score is 1.28 (approx).

ME = 1.28*0.051 = 0.066

Therefore, the approximate width of the 80% confidence interval is ±0.066.

The best choice is C.

What Is the Approximate Width of an 80 Percent Confidence