Question

a survey finds 52% of surveyed voters plan to vote for smith with a margin of error of 1% at a 95% confidence level. what is the correct interpretation for the confidence interval? a if the same survey were done repeatedly, 95% confidence exists that the proportion of the population voting for smith is between 51% and 53%. b the voters are sure that smith has 95% chance of winning the election. c smith has between 94% and 96% chance of winning the election. d the person doing the survey is 95% sure that the survey was done correctly.

Explanation:

Step1: Recall confidence - interval concept

A confidence interval gives a range of values within which the true population parameter is likely to lie. In a proportion - based survey, if 52% of surveyed voters plan to vote for Smith with a margin of error of 1%, the 95% confidence interval for the proportion of the population voting for Smith is calculated as $\hat{p}\pm E$, where $\hat{p}$ is the sample proportion and $E$ is the margin of error. Here, $\hat{p} = 0.52$ and $E=0.01$.

Step2: Calculate the confidence interval

The lower limit of the confidence interval is $0.52 - 0.01=0.51$ or 51%, and the upper limit is $0.52 + 0.01 = 0.53$ or 53%. This means that we are 95% confident that the proportion of the population voting for Smith is between 51% and 53%.

Answer:

A. If the same survey were done repeatedly, 95% confidence exists that the proportion of the population voting for Smith is between 51% and 53%.