Simple random sampling has been used to obtain a sample of size 60 from a population of size 500. The sample proportion was 0.7. An approximate 95% confidence interval for the population proportion is
A) 0.500 to 0.700
B) 0.750 to 0.810
C) 0.588 to 0.812
D) 0.638 to 0.762

Question

Quizplus · Accepted Answer

We can use the formula for the confidence interval for a proportion:
p ± z*sqrt(p(1-p)/n)
where p is the sample proportion, n is the sample size, and z* is the z-score corresponding to the desired level of confidence. Since we want a 95% confidence interval, z* is the 1.96 z-score.

Plugging in the values, we get:
0.7 ± 1.96*sqrt(0.7(1-0.7)/60)
0.7 ± 0.106
The lower bound of the interval is 0.7 - 0.106 = 0.594 and the upper bound is 0.7 + 0.106 = 0.806. Therefore, the approximate 95% confidence interval for the population proportion is (0.588, 0.812), which corresponds to choice C.

Simple Random Sampling Has Been Used to Obtain a Sample