A politician wants to estimate the percentage of people who like his new slogan. Given that no prior estimate of the population proportion is available, what is the minimum sample size such that the margin of error is no more than 0.08 for a 95% confidence interval?
A) 105.70
B) 106
C) 150.06
D) 151

Question

Quizplus · Accepted Answer

The formula for minimum sample size can be written as:
n = [Z^2 * p *(1-p)] / E^2 
Where:
Z = the Z-score associated with the desired level of confidence (in this case, 1.96 for 95% confidence)
p = the estimated proportion of the population that likes the slogan (since no prior estimate is available, we use 0.5 as a conservative estimate)
E = the desired margin of error (0.08 in this case)

Substituting these values into the formula, we get:
n = [1.96^2 * 0.5 * (1-0.5)] / 0.08^2
n ≈ 151

Therefore, the minimum sample size required to achieve a margin of error no more than 0.08 for a 95% confidence interval is 151.

A Politician Wants to Estimate the Percentage of People Who