Suppose you ran 50 separate simulations. Each of these simulations represent a week (7 days) of working with a molding machine. During each simulation, the average number of the machine's failures per day was recorded. You observed that the mean of all of your sample means follows a normal distribution with a standard deviation of 25 that is, ~N(M, 25). Later you decided to run a hypothesis testing on the population mean with the assumptions below and an alpha = 0.01.

H0:The population mean is equal to 20

H1:The population mean is not equal to 20

What would be the lowest and highest values of the sample mean that would allow you to not reject the null hypothesis?

Lowest value?

Highest Value?