A researcher wants to estimate the proportion of manufacturing companies that use the six sigma method.For this purpose, she will take a random sample of 50 manufacturing companies and find out how many of them use this method.She estimates that the proportion will be anywhere from 0.4 to 0.55.Of all the proportions in that range, which one would produce the widest 95% confidence interval for the population proportion?
A)0.4
B)0.45
C)0.5
D)0.55
E)0.6

Question

Quizplus · Accepted Answer

The widest 95% confidence interval for a proportion occurs when the proportion is 0.5. This is because the formula for the confidence interval width is influenced by the term $p(1-p)$, which reaches its maximum value when $p = 0.5$.

A Researcher Wants to Estimate the Proportion of Manufacturing Companies