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)± 0.196
B)± 0.164
C)± 0.480
D)± 0.206

Question

Quizplus · Accepted Answer

To find the width of the confidence interval, we need to use the formula:
Margin of Error = Z*sqrt(p(1-p)/n)
where Z corresponds to the level of confidence, p is the sample proportion, and n is the sample size.

Since we have 12 successes in a sample of 25, the sample proportion is p = 12/25 = 0.48.
For a 90% confidence interval, the corresponding Z value is 1.645.
Plugging these values into the formula, we get:
Margin of Error = 1.645*sqrt(0.48*0.52/25) = 0.082

So the width of the confidence interval is approximately ±0.082.
Rounding to three decimal places gives us ±0.164, which is closest to choice (B).

What Is the Approximate Width of a 90 Percent Confidence