Question

1 In the November 2016 election, Donald Trump received 49% of the votes cast in Florida (Hillary Clinton received 47%). Many news organizations conduct surveys before elections to try to predict the winner. Suppose a survey was conducted in Florida shortly before the election such that we can assume that the true proportion of the population who planned to vote for Trump was 49%. The pollsters surveyed 600 likely voters and found that 283 of them planned to vote for Trump. A What was the sample proportion? Give your answer as a decimal and a percentage. B What is the standard error for the sampling distribution of the sample proportion in this case? C What is the margin of error for a 95% confidence level? Interpret the margin of error. D Give the lower and upper limits of the 95% confidence interval for the population proportion, p, of voters who planned to vote for Trump based on the sample. Interpret the confidence interval. E Based on this interval, would Trump getting less than half of the vote in Florida have been surprising? Explain briefly. F Pollsters often use larger sample sizes just before an election. What effect does increasing the sample size have on the width of the confidence interval? Why do you think pollsters do this?

Answer 1

Soluion 283 6OD 47.2. P-P) 0.49 (1-D49) 0.0204 tithe &tandand deıad'ou o8 le fample. Catical value at qs y conholenie (Zu) - This is tte conhcenee mterval, in hieh wrichth Limi «ррег 0.S12 Lower limit -p- ME 0.472- 0.04D= 0.432 Heni e Cenbidenie Juterval:(0.43 2, 0.Si2) conbidlent that he tue mea Prporh) we are 95. Vote that orald ump geceiveg wil lie in Hur intervaf. NO, because, ue poporhim ues i^ As onbrolence inderral use karger somple Sze, it w give and he ean Poeoliet more асailys