A high-tech company wishes to estimate the mean number of years of college education its employees have completed. A good estimate of the standard deviation for the number of years of college is 1.0. How large a sample needs to be taken to estimate μ to within 0.5 years with 99 % confidence?

I know the formula, but it requires you know the pop. mean and sample mean. But there isn't any in the question. How do I do it?

Question

A high-tech company wishes to estimate the mean number of years of college education its employees have completed. A good estimate of the standard deviation for the number of years of college is 1.0. How large a sample needs to be taken to estimate μ to within 0.5 years with 99 % confidence?

I know the formula, but it requires you know the pop. mean and sample mean. But there isn't any in the question. How do I do it?

kropot72 · Answer

The margin of error is the distance from x bar, the center of the confidence interval, to the end of the interval. The margin of error is given as 0.5 years.
$$0.5=z \times \frac{\sigma}{\sqrt{n}}$$
$$0.5=\frac{2.576}{\sqrt{n}}$$
z is 2.576 to find a 99% confidence level.
Now can you solve to find n?

kropot72 · Answer

@wjannie do you understand?