Question

To estimate the proportion of city voters who will vote for the Republican candidate in the election, two students, Manny and Nina, each decide to conduct polls in the city. Manny selects a random sample of 50 voters, while Nina selects a random sample of 100 voters. Suppose both samples result in 48% of the voters saying they will vote for the Republican candidate. Whose 95% confidence interval will have the larger margin of error: Manny’s or Nina’s? How are you deciding?

Answer 1

Manny's 95% confidence interval would have the larger margin of error.

The smaller the sample size the larger the margin of error. Manny's sample size is smaller than Nina's.

Explanation:

Margin of error for the confidence interval of a proportion is given as z[sqrt (p(1-p) ÷ n)]

z is test statistic

p is sample proportion

n is sample size

From the formula above, the relationship between margin of error and sample size is inverse in which decrease in one quantity (sample size) leads to a corresponding increase in the other quantity (margin of error)

Manny's sample size is 50 while Nina's is 100.

Therefore, Manny's 95% confidence interval would have the larger margin of error because her sample size is smaller.