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26.07.2020 •
Mathematics
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 60%. You would like to be 98% confident that your estimate is within 2.5% of the true population proportion. How large of a sample size is required?
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Ответ:
A sample size of 2080 is needed.
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:
98% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
Based on previous evidence, you believe the population proportion is approximately 60%.
This means that![\pi = 0.6](/tpl/images/0713/4215/09971.png)
How large of a sample size is required?
We need a sample of n.
n is found when
. So
Rounding up
A sample size of 2080 is needed.
Ответ: