Exhibit 22-4
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 22-4. 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

To calculate the confidence interval, we can use the formula:

Sample Proportion ± (Z α/2 * Standard Error)

Z α/2 is the critical value for the desired level of confidence, which is approximately 1.96 for 95% confidence interval.

Standard Error = sqrt((p*q)/n), where p is the sample proportion, q is 1-p, and n is the sample size.

Plugging in the given values, we get:

0.7 ± (1.96 * sqrt((0.7*0.3)/50))

Simplifying the calculation, we get:

0.7 ± 0.124

Therefore, the 95% confidence interval is (0.576, 0.824).

The best choice is C.

Exhibit 22-4 Simple Random Sampling Has Been Used to Obtain a Sample