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Ryan, Engineer

Category: Calculus and Above

Satisfied Customers: 9046

Experience: B.S. in Civil Engineering

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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?

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