A chemist was interested in examining the effects of four chemicals on a chemical process yield. Letxi,i= 1, 2, 3, 4 represent the effects of the four chemicals, respectively andybe the process yield. The chemist's first instinct was to include each of the chemicals in the equation in a linear fashion.

Initial Model:y=0+1x1+2x2+3x3+4x4+

The regression equation is:= 229 + 12.5x1- 39.2x2+ 2.69x3- 33.9x4

Analysis of Variance

Source

DF

SS

MS

F

p-value

Regression

4

18969.7

4742.4

19.71

0.007

Residual Error

4

962.5

240.6

Total

8

19932.2

After the initial analysis, the chemist decided to remove chemicals 2 and 3 from the model.

Revised Model:y=0+1x1+4x4+

The regression equation is:= 122 + 6.82x1- 14.2x4

Analysis of Variance

Source

DF

SS

MS

F

p-value

Regression

2

18385.7

9192.9

35.67

0.000

Residual Error

6

1546.5

257.8

Total

8

19932.2

To test the hypothesisH0: 2= 3= 0 vs.Ha: At least one of2or3is not 0 at 5% level of significance, which critical value should be used?