Question

Suppose that two polls are conducted to estimate what proportion of the overall electorate will vote Democratic in the 2022 midterms. One of the polls has a sample size of n=250, where r=115 of the respondents planned on voting for the Democrats. The other poll has a sample size of n=1000, where r=480 of the respondents planned on voting for the Democrats. Based off of this information, which of the following proportions is MOS' likely to be the closest to the actual proportion of voters that vote Democratic in 2022 ?

A) 46%
B) 48%
C) both will be accurate
D) neither will be accurate

Answer 1

To determine the closest proportion to the actual proportion of voters that vote Democratic in 2022, we calculate the confidence intervals for each poll. The second poll with a sample size of 1000 and 480 respondents planning to vote Democratic is likely to be the closest, with a proportion of 48% and a narrower margin of error.

Step-by-step explanation:

To determine which proportion is likely to be closest to the actual proportion of voters that vote Democratic in 2022, we need to find the confidence intervals for each poll. Confidence intervals give a range of values within which the true proportion is likely to fall.

For the first poll with a sample size of 250 and 115 respondents planning to vote Democratic, we can calculate the proportion as 115/250 = 0.46 or 46%. The margin of error can be calculated as 1.96 * sqrt(0.46 * (1-0.46) / 250) = 0.063 or 6.3%. So the confidence interval for this poll is (46% - 6.3%, 46% + 6.3%) = (39.7%, 52.3%).

For the second poll with a sample size of 1000 and 480 respondents planning to vote Democratic, the proportion is 480/1000 = 0.48 or 48%. The margin of error can be calculated as 1.96 * sqrt(0.48 * (1-0.48) / 1000) = 0.028 or 2.8%. So the confidence interval for this poll is (48% - 2.8%, 48% + 2.8%) = (45.2%, 50.8%).

Based on the confidence intervals, the second poll with a proportion of 48% and a narrower margin of error is likely to be the closest to the actual proportion of voters that vote Democratic in 2022.