SOLUTION: A political candidate has asked you to conduct a pole to determine what percentage of people support her. If the candidate only wants a 4% margin of error at a 90% confidence leve

Question 1201568: A political candidate has asked you to conduct a pole to determine what percentage of people support her.
If the candidate only wants a 4% margin of error at a 90% confidence level, what size of sample is needed?
Found 2 solutions by Glaviolette, math_tutor2020:
Answer by Glaviolette(140) (Show Source): You can put this solution on YOUR website!

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answer: 423

Explanation:

At 90% confidence, the z critical value is roughly z = 1.645
Use a table like this
https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf
to get that value. Look at the bottom row labeled "Z" and above the 90% confidence level.
A stats calculator can also compute this value.

We aren't told the phat value (sample proportion), so the best we can do is make a conservative estimate of phat = 0.5

We want the margin of error to be 4%, so E = 0.04

Summary input values:
z = 1.645 approximate
phat = 0.5
E = 0.04

We can now calculate the min sample size.
n = phat*(1-phat)*(z/E)^2
n = 0.5*(1-0.5)*(1.645/0.04)^2
n = 422.816406 approximately
n = 423 always round UP to the nearest whole number

That's how we arrive at the final answer of 423.

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