The Jacobs Chemical Company wants to estimate the mean time (minutes) required to mix a batch of material on machines produced by three different manufacturers. To limit the cost of testing, four batches of material were mixed on machines produced by each of the three manufacturers. The times (in minutes) needed to mix the material follow.

Manufacturer 1 Manufacturer 2 Manufacturer 3

192719

252518

233022

212621

(a)

Define all variables.

x1 x2 Manufacturer

?01

1?2

0?3

Write a multiple regression equation that can be used to analyze the data.

E(y)=

(b)

What are the best estimates of the coefficients in your regression equation?

b0=b1=b2=

(c)

In terms of the regression equation coefficients, what hypotheses must we test to see whether the mean time to mix a batch of material is the same for all three manufacturers?

H0: b1= b2=0

Ha: One or more of the parameters is not equal to zero.H0: b0!=0

Ha: b0=0 H0: One or more of the parameters is not equal to zero.

Ha: b1= b2=0H0: b0=0

Ha: b0!=0

(d)

For an a =0.05 level of significance, test to see whether the mean time to mix a batch of material is the same for all three manufacturers.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =