The .95 confidence interval for a population proportion based on a sample of n cases ranged from .40 to .56.If the sample proportion was unchanged, but the sample size was increased to 4n, the .95 confidence interval would be about
A) .32 to .64.
B) .36 to .60.
C) .44 to .52.
D) .46 to .50.

Question

Quizplus · Accepted Answer

The formula for calculating the confidence interval for a population proportion is:

CI = sample proportion +/- margin of error

where the margin of error can be calculated as:

margin of error = z* * sqrt[(sample proportion * (1 - sample proportion))/n]

where z* is the z-score corresponding to the desired level of confidence.

Given that the original confidence interval had a range of 0.56 - 0.40 = 0.16 and the sample size is increased to 4n, we can calculate the new margin of error as:

margin of error = 1.96 * sqrt[(0.48 * 0.52)/(4n)] = 0.049

where we have used the fact that the original sample proportion was (0.40 + 0.56)/2 = 0.48.

Thus, the new confidence interval will be:

CI = 0.48 +/- 0.049

CI = (0.431, 0.529)

which rounds to (0.44, 0.52) at the .95 confidence level. Therefore, the best choice is C.

The 95 Confidence Interval for a Population Proportion Based on a a Sample