Joe Candidate’s polling organization finds that in a random sample of 900 voters, 500 prefer Joe to his rival candidate in a two-person race. In your calculations, round answers to two decimal places.

a) What proportion of voters prefers Joe?

b) Compute the variance and standard deviation of the proportion. What is the standard error?

c) What are the UCL and LCL for a 95% confidence interval for the proportion preferring Joe? What do you predict about the race?

d) What are the UCL and LCL for a 99% confidence interval for the proportion preferring Joe? What do you predict about the race?

e) Would your conclusion be different if the sample size were 400 and the proportion were the same as in the original problem? (Carry out this calculation to three decimal places.)
What about a sample of 1,600?

f) What would you conclude if the sample size were 900 but the number of respondents who favor Joe were (i) 460? (ii) 700?