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Answer:
We need a sample of size at least 13.
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:
90% confidence interval: (0.438, 0.642).
The proportion estimate is the halfway point of these two bounds. So
95% confidence level
So , z is the value of Z that has a pvalue of
, so
.
Using the information above, what size sample would be necessary if we wanted to estimate the true proportion to within ±0.08 using 95% confidence?
We need a sample of size at least n.
n is found when M = 0.08. So
Rounding up
We need a sample of size at least 13.