Question

Sheer industries is considering a new computer-assisted program to train maintenance employees to do machine repairs. In order to fully evaluate the program, the director of manufacturing requested an estimate of the population mean time required for maintenance employees to complete the computer assisted training. Use 7.64 days as a planning value for the population standard deviation. (Round your answers up to the nearest whole number.) (a) Assuming 95% confidence, what sample size would be required to obtain a margin of error of 0.5 days?

Answer 1

The minimum sample size to have this margin of error is n = 897.

Explanation:

We have to estimate a parameter with a confidence interval. The confidence level is 95% and the margin of error is 0.5 days.

The population standard deviation is 7.64 days.

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

We have to calculate the minimum sample size.

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 7.64)/(0.5)\right)^2=(29.95)^2=896.9\approx 897`

The minimum sample size to have this margin of error is n = 897.