Question is in the decription.

Question

A survey is done by a news agency for presidential elections. The agency reported that the Reds are

leading Blues by 11%, because 48% of the participants supported Red Party’s candidate while 37% supported

Blue Party’s candidate. Note that 400 people participated in the survey and the population size is

significantly larger than 400.

a) What margin of error should be reported for each candidate’s estimated vote rate?

b) What margin of error should be reported for the estimated lead?

c) Which candidate’s margin of error is larger than the other? Explain the reason.

d) How would margin of errors change if there were 1800 participants in the survey? Briefly explain.

NOTE: Use 95% confidence interval for calculating margin of errors.

Answer 1

a. E = z(𝜶/2)√(pq/n) = 1.96√(.37)(.48)/400 = .0413 for each candidate

b. The margin of error is calculated the same way for both candidates so the margin of error will be the same for the leading candidate and for the trailing candidate.

c. Each candidate has the same margin of error because they are calculated with the same formula

d. E = z(𝜶/2)√(pq/n) = 1.96√(.37)(.48)/400 = .0413

E = z(𝜶/2)√(pq/n) = 1.96√(.37)(.48)/1800 = .0195

As you increase the number of participants in the survey the margin of error decreases.