Question

Which distribution do you use when you are testing a population mean and the population standard deviation is known? Assume a normal distribution, with $n\ge 30$.

Short answer

When we are testing a population mean and when the population standard deviation is known we use normal distribution i.e. $\mathcal{N}\left({\mu }_X,{\sigma }_X/\sqrt{n}\right)$.

Step-by-step solution

Population variance.

The root of the variance of a collection of integers is employed to calculate the population variance.

It's wont to calculate a confidence interval before making a call (such as accepting or rejecting a hypothesis).

Sample variance could be a slightly more complicated computation.

Find distribution when testing population means and population variance.

The normal distribution is employed when testing a population mean and when the population variance is understood.

That's to mention, $\mathcal{N}\left({\mu }_X,\frac{{\sigma }_X}{\sqrt{n}}\right)$