that you precisely label the Critical Region $($set of values of the sample statistic pertinent to

rejection of $H_0,$ the null hypothesis$).$ Explain the primary difference between Type $1$ and Type

$2$ errors and which of them is likely to cause a greater problem for an Operations Manager

$/$Industrial Engineer?

Given the following process control data for a normally distributed quality variable $($three

samples of size four each$)$:

If the process is known to have a mean of $15$ and a standard deviation of $3,$ what are the $3$ upper

and lower control limits for an x$-$Bar $($Sample Mean$)$ chart?