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Answer:
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