# Statistics

An investigator wants to estimate caffeine consumption in high school students. How many students would be required to ensure that a 95% confidence interval estimate for the mean caffeine intake is within 15mg of the true mean? Assume the standard deviation in caffeine intake is 68mg. How many students would be required to estimate the proportion of students who consume coffee. Suppose we want the estimate to be within 5% of the true proportion with 95% confidence.

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1. Use formulas to find sample size.

For the first part:

n = [(z-value * sd)/E]^2
...where n = sample size, z-value will be 1.96 using a z-table to represent the 95% confidence interval, sd = 68, E = 15, ^2 means squared, and * means to multiply.

For the second part:

n = [(z-value)^2 * p * q]/E^2
... where n = sample size, z-value is 1.96, p = .5 (when no value is stated in the problem), q = 1 - p, ^2 means squared, * means to multiply, and E = .05 (for 5%).

Plug the values into the formulas and finish the calculations. Round your answers to the next highest whole number.

Hope this helps.

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