Question

A large city in a Western State has always believed that 60% of its citizens support the addition of an ombudsmen among its city council members. However, under the new mayor, there is doubt that this proportion continues to hold. They poll 1600 people, and plan to construct a 95% confidence interval. Suppose 50% of those polled support the addition of an ombudsman. Give the number you would add or subtract to the point estimate to build this interval.   (

Answer 1

Let P be the population proportion of citizens that support the addition of an ombudsmen.

p denote the sample proportion.   p= 0.5

n denote the sample size.   n=1600

We know that expected value of sample proportion is population proportion. That is, E( p ) = P

And standard deviation is

Hence, using Central limit theorem, follows Standard Normal distribution.

To find the confidence interval we estimate the variance using sample proportion.

Hence, standard deviation is

95% confidence interval for population proportion is:

where, is such that

= 1.96

Hence, the number we would add or subtract to the sample proportion to build above interval is

Hence, we would add or subtract 0.0245 to the point estimate to build the 95% confidence interval for P.

I hope you find the solution helpful. If you have any doubt then ask in the comment section.

Please do not forget to vote the answer.

Thank you in advance!!!