A researcher wants to estimate the proportion of a population which possesses a given characteristic.A random sample of size 200 is taken and 30% of the sample possesses the characteristic.The 95% confidence interval to estimate the population proportion is ___.
A)0.53 to 0.67
B)0.25 to 0.35
C)0.24 to 0.36
D)0.27 to 0.33
E)0.28 to 0.34

Question

Quizplus · Accepted Answer

To estimate the population proportion, we can use the sample proportion along with the appropriate margin of error at a given confidence level.

First, we calculate the standard error:

SE = sqrt [(p-hat * (1 - p-hat)) / n]
SE = sqrt [(0.3 * 0.7) / 200]
SE = 0.034

Next, we calculate the margin of error at 95% confidence level using the z-score:

ME = z* SE
ME = 1.96 * 0.034
ME = 0.067

Finally, we construct the confidence interval by adding and subtracting the margin of error from the sample proportion:

CI = p-hat ± ME
CI = 0.3 ± 0.067
CI = (0.24, 0.36)

Therefore, the 95% confidence interval to estimate the population proportion is 0.24 to 0.36, which is choice C.

A Researcher Wants to Estimate the Proportion of a Population