Using the margin of error for the z-distribution, the sample sizes are given as follows:
a) 822.
b) 1068.
<h3>What is a confidence interval of proportions?</h3>A confidence interval of proportions is given by:
The margin of error is given by:
In which:
is the sample proportion.
- z is the critical value.
- n is the sample size.
We have a 95% confidence level, hence, z is the value of Z that has a p-value of
, so the critical value is z = 1.96.
Item a:
The estimate is of , hence we solve for n when M = 0.03.
n = 821.2
A sample of 822 is needed.
Item b:
No prior estimate, hence .
n = 1067.11
A sample of 1068 is needed.
More can be learned about the z-distribution at brainly.com/question/25890103
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