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Chris3529
19.02.2020 •
Mathematics
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.
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Ответ:
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![\sqrt{\pi(1-\pi)}](/tpl/images/0515/9495/e4d4f.png)
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
Ответ:
i think the correct answer is f