Exhibit 21-4
Simple random sampling has been used to obtain a sample of size 50 from a population of size 500. The sample proportion was 0.7.
-Refer to Exhibit 21-4. An approximate 95% confidence interval for the population proportion is
A)0.500 to 0.700
B)0.750 to 0.810
C)0.576 to 0.824
D)0.638 to 0.762

Question

Quizplus · Accepted Answer

The formula for the confidence interval for a proportion is:
sample proportion +/- z* (standard error)
where z* is the critical value from the standard normal distribution for the desired level of confidence (in this case, 95%).

The standard error of the proportion is:
sqrt[(sample proportion * (1 - sample proportion)) / sample size]

Plugging in the values we have:
sample proportion = 0.7
sample size = 50
z* for 95% confidence is approximately 1.96 (from the standard normal table)

standard error = sqrt[(0.7 * 0.3) / 50] = 0.084

Confidence interval = 0.7 +/- 1.96*(0.084) = 0.576 to 0.824

So the best choice is C.

Exhibit 21-4 Simple Random Sampling Has Been Used to Obtain a Sample