We would like to create a confidence interval.
Which of the following would produce the smallest margin of error? Select one:

a. A 99% confidence level and a sample size of 50 subjects.

b. A 90% confidence level and a sample size of 50 subjects.

c. A 90% confidence level and a sample size of 300 subjects.

d. A 99% confidence level and a sample size of 300 subjects.

c.A 90% confidence level and a sample size of 300 subjects.

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 , we have the confidence interval with a margin of error of:

In which

z is the zscore that has a pvalue of .

In this problem

The proportions are the same for all the options, so we are going to write our margins of error as functions of

So

a.A 99% confidence level and a sample size of 50 subjects.

99% confidence interval

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

The margin of error is

b.A 90% confidence level and a sample size of 50 subjects.

90% confidence interval

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

The margin of error is

c.A 90% confidence level and a sample size of 300 subjects.

90% confidence interval

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

The margin of error is

This produces smallest margin of error.

d.A 99% confidence level and a sample size of 300 subjects.

99% confidence interval

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

The margin of error is

i think that you should ask google for the answer to that problem because if we don't know it google does