Question

(Q3, 5 parts) A journalist plans to take a poll estimating the proportion of people who plan to vote for his favorite politician in an upcoming election.

(a) How large of a sample is needed to guarantee a 90% confidence interval with a 6% margin of error?

(b) The journalist randomly polls just 50 people and finds 28 plan to vote for his candidate. Construct a 90% confidence interval for him based on his data.

(c) Properly Interpret the confidence interval for the journalist (who probably isn't listening)

(d) The journalist concludes that since his predicted proportion (28/50) is 6% above 50%, his candidate is supported by a majority of voters. Use z-scores to determine what level of confidence he can state this prediction at. (Note: You've never done this before. What I want you to do is use the sample size formula to solve for z using algebra; Then use the context to plug in for the other values; Finally, use normalcdf to find the area between -z and +z.))

(e) Meanwhile, a statistician takes a poll of 1200 voters and finds 55% of them support the opposite candidate. Construct a 99% confidence interval and interpret the interval in the context of the problem.

Answer 1

a) We will assume that the proportion is 0.5

a) for 90% confidence

Margin of error = 0.06

b)point estimate for the proportion :

for 90% confidence

c) We are 90% confident that the proportion of people who plan to vote for his favourite politician in an upcoming election is between

e)

the point estimate for the proportion :

for 99% confidence

We are 99% confident that the proportion of people who plan to vote for the opposite candidate in an upcoming election is between