A mayoral candidate in a large metropolitan area has hired you to take a poll to determine the proportion of registered voters who plan to vote for him. He would like you to report a 95% confidence interval with a margin of error no more than 0.04. Whiat is the smallest sample size that will produce an interval with these specifications?

The smallest sample size that will produce an interval with these specifications is 601.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

The margin of error is:

95% confidence level

So , z is the value of Z that has a pvalue of , so .

He would like you to report a 95% confidence interval with a margin of error no more than 0.04. What is the smallest sample size that will produce an interval with these specifications?

We have to find n for which M = 0.04.

We dont know the true proportion, so we use , which is when the smallest sample size needed will have it's largest value.

Rounding up

The smallest sample size that will produce an interval with these specifications is 601.

answer: no, but if it does it's a obvious pattern.

step-by-step explanation: