A room in a laboratory is only considered safe if the mean radiation level is 400 or less. When a sample of 10 radiation measurements were taken, the mean value of the radiation was 414 with a standard deviation of 17. There are concerns that mean radiation is above 414.

A room in a laboratory is only considered safe if the mean radiation level is 400 or less. When a sample of 10 radiation measurements were taken, the mean value of the radiation was 414 with a standard deviation of 17. There are concerns that mean radiation is above 414. Radiation levels in the lab are known to follow a normal distribution with standard deviation 22. We will like to conduct a hypothesis test at the 5% level of significance to determine whether there is evidence that the laboratory is unsafe.

What will be the appropriate test?