In: Math
A national television network took an exit poll of 1460 voters after each had cast a vote in a state gubernatorial election. Of them, 680 said they voted for the RepublicanRepublican candidate and 780 said they voted for the DemocraticDemocratic candidate. Treating the sample as a random sample from the population of all voters, a 95% confidence interval for the proportion of all voters voting for the DemocraticDemocratic candidate was (0.509, 0.560). Suppose the same proportions resulted from n=146146 (instead of 146), with counts of 68 and 78, and that there are only two candidates. Complete parts a and b below.
a. Does a 95% confidence interval using the smaller sample size allow you to predict the winner? Explain.
The 95% confidence interval for the proportion of all voters voting for the DemocraticDemocratic candidate is (____, _____). Now a 95% confidence interval (does, does not) allow you to predict the winner, since this interval (does not include, includes) (0,1, or 0.5).