Question

1. Imagine that a survey was conducted in Florida on the day before the November 2008 election. Pollsters surveyed a random sample of 600 likely voters and found that 321 of them planned to vote for Obama.

(a) What is the sample proportion? Give your answer as a decimal.

(b) What is the lower limit of the 95% confidence interval?

(c) What is the upper limit of the 95% confidence interval?

(d) Write a sentence explaining the meaning of the interval in the context of the problem.

(e) Based on the interval from part (e), would it have been surprising if Obama had received less than half of all votes in Florida? Give a reason for your answer.

(f) The poll was conducted a day before the election, so its results should have represented what happened in the election well. In the end, Obama received 51% of the vote. Was the final vote percentage in Florida consistent with the confidence interval? Explain your answer.

Answer 1

Let p denotes the true proportion of people who planned to vote for Obama.

a) The sample proportion is

b) The lower limit of the 95% confidence interval = 0.502

c) The upper limit of the 95% confidence interval = 0.568

d) Interpretation of 95% confidence interval -

Among 100 samples drawn, sample proportion will lie between (0.502, 0.568) for 95 samples.

e) Since lower bound of the confidence interval > 0.5, so it would have been surprising if Obama had received less than half of all votes in Florida.

f) Since 0.51 lies inside the interval, the final vote percentage in Florida was consistent with the confidence interval