Dimensions
the Dimensions of a Two by Four Board Are $\mu$

Dimensions
The dimensions of a two by four board are not actually two inches by four inches.Rather the actual dimensions are supposed to be 1.50 inches by 3.50 inches.A planer finishes the boards to the proper dimensions.To maintain quality control,periodic checks are made to see that the planer is set to the correct dimension.When the planer is adjusted properly,the average width is $\mu$ = 3.5 inches.If the average width is not 3.5 inches,the planer must be adjusted.Thus the null hypothesis is $\mu$ = 3.5 inches and the alternate hypothesis is $\mu \neq$ 3.5 inches.For control purposes,a random sample of 49 boards is taken twice daily.The standard deviation of the process is $\text { σ }$ = 0.25 inches.To minimize the unnecessary adjustment of the planer,the risk of a Type I error, $\alpha$ ,is set at 0.05.
-Determine the lower and upper critical values for $\bar { x }$ .
Lower value = ____________________
Upper value = ____________________