Question

A software developer wants to know how many new computer games people buy each year. Assume a previous study found the standard deviation to be 1.7. She thinks the mean is 6 computer games per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.14 at the 95% level of confidence? Round your answer up to the next integer.

Answer 1

The minimum sample size required to ensure that the estimate has an error of at most 0.14 at the 95% level of confidence is n=567.

Explanation:

We have to calculate the minimum sample size n needed to have a margin of error below 0.14.

The critical value of z for a 95% confidence interval is z=1.96.

To do that, we use the margin of error formula in function of n:

`MOE=(z\cdot \sigma)/(√(n))\\\\\\n=\left((z\cdot \sigma)/(MOE)\right)^2=\left((1.96\cdot 1.7)/(0.14)\right)^2=(23.8)^2=566.42\approx 567`

The minimum sample size to have this margin of error is n = 567.