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

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

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

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

The larger sample size helps to reduce​ people's bias for onecandidate or the other.The proportions of people who voted for theDemocratic and Republican candidates would be different from thoseabove.    The​ z-scores in the confidenceintervals would be different for this confidence interval fromthose above.We have a larger margin of error when we have a largersample​ size, giving us more precision to estimate theparameter. The larger sample size provides more​ information, sowhen I have the same amount of​ confidence, I have more precisionto estimate the parameter.