Question

In one exit poll of n​ = 140​ voters, 66 said they voted for the Democratic candidate and 74 said they voted for the Republican candidate.

(a) Does a​ 95% confidence interval for the proportion voting for the Democratic candidate allow you to predict the​ winner? Why or why​ not?

​No, because some of the values in the interval are negative​ (less than​ 0) or greater than​ 1, depending on whether we define the proportion to be voting for the Republican or Democratic candidate.​No, because the interval includes a majority of people voting for the Democratic candidate and a majority of people voting for the Republican candidate.    Yes, because the interval includes a majority of people voting for the Democratic candidate and a majority of people voting for the Republican candidate​ (proportions both above and below​ 0.5).​Yes, because the interval ​doesn't include both values greater than 0.5 and values less than 0.5.​No, because the interval ​doesn't include values greater than 0.5​ (a majority of people voting for the Democratic​ candidate) and values less than 0.5​ (a majority of people voting for the Republican​ candidate). ​Yes, because all the values in the interval are positive​ (greater than​ 0) and less than 1.

(b) A​ 95% confidence interval with n​ = 1400 voters and counts 660 and 740 would give different results than those above. Explain why.

The larger sample size helps to reduce​ people's bias for one candidate or the other.The proportions of people who voted for the Democratic and Republican candidates would be different from those above.    The​ z-scores in the confidence intervals would be different for this confidence interval from those above.We have a larger margin of error when we have a larger sample​ size, giving us more precision to estimate the parameter. The larger sample size provides more​ information, so when I have the same amount of​ confidence, I have more precision to estimate the parameter.

Answer 1