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Ryan
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In a college student poll, it is of interest to estimate the
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In a college student poll, it is of interest to estimate the proportion p of students in favor of changing from a quarter system to a semester system. How many students should be polled so that we can estimate p to within .09 using a 99% confidence interval?
Submitted:
1 year ago.
Category:
Calculus and Above
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Expert:
Ryan
replied 1 year ago.
Hi,
Welcome! Thank you for using the site.
I'll be happy to help you with this problem.
The formula for calculating the minimum sample size is:
n = p(1  p)(z/E)^2
where p is the population proportion, z is the critical value for the given confidence level, and E is the desired margin of error.
When p is not known, a conservative estimate (i.e. the largest sample size) is found by using p = 0.5.
For a 99% confidence level, use z = 2.576.
With E = 0.09, the required sample size is:
n = (0.5)(1  0.5)(2.576 / 0.09)^2 = 204.8
Since a sample size must be an integer value, and the calculated value is a minimum, it must be rounded UP to the next integer value: 205
Required sample size = 205
Please feel free to ask if you have any questions about this solution.
Thanks,
Ryan
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