SOLUTION: You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 40%. You would like to be 95% co
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Question 1194721: You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 40%. You would like to be 95% confident that your estimate is within 1.5% of the true population proportion. How large of a sample size is required?
I am having trouble setting up this problem correctly. I know that the z-score is 1.960 Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
You have the correct approximate z value
z = 1.960 when we have a 95% confidence level
For any future students curious how to find this value, you would use a table such as this one https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf
Locate the "95%" in the bottom row. Just above that is 1.960
Alternatively, you can use a calculator to determine the value of z.
E = 0.015 is the decimal form of the 1.5% error we're after. We want this error or smaller.
p = 0.40 based on a previous study
n = min sample size needed
n = p*(1-p)*(z/E)^2
n = 0.40*(1-0.40)*(1.960/0.015)^2
n = 4097.70666666667 approximately
n = 4098
Always round up to the nearest whole number.
If we got something like 4097.00001, we still round up to the nearest whole number 4098 to ensure we clear the hurdle.
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