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21.02.2020 •
Mathematics
Exercise 6.13 presents the results of a poll evaluating support for the health care public option in 2009, reporting that 52% of Independents in the sample opposed the public option. If we wanted to estimate this number to within 1% with 90% confidence, what would be an appropriate sample size?
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Ответ:
A sample size of 6755 or higher would be appropriate.
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 M is given by:
90% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
52% of Independents in the sample opposed the public option.
This means that![p = 0.52](/tpl/images/0519/5358/6ce1d.png)
If we wanted to estimate this number to within 1% with 90% confidence, what would be an appropriate sample size?
Sample size of size n or higher when
. So
A sample size of 6755 or higher would be appropriate.
Ответ: