Question

In: Statistics and Probability

Use computer software packages, such as Excel, to solve this problem. The Jacobs Chemical Company wants...

Use computer software packages, such as Excel, to solve this problem.

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 needed to mix the material follow.

Manufacturer 1 Manufacturer 2 Manufacturer 3
17 29 17
23 27 16
21 32 20
19 28 19

a. The following regression model can be used to analyze the data.

E(y) = B0+B1D1+B2D2

Show the values of the variables below. If your answer is zero enter “0”.

D1 D2 Manufacturer
0 0 1
1 2
0 3

b. Show the estimated regression equation (to the nearest whole number and enter negative value as negative number).

y^=______+______D1 +_______D2

      

c. What null hypothesis should we test to determine if we should reject the assumption that the mean time to mix a batch is the same for all three manufacturers?

Select the number of the null hypothesis you would want to test.

- Select your answer -12345Item 6

d. What is the value of the test statistic in your hypothesis in part (c) (to 2 decimals)? Use Table 4 in Appendix B.

What is the -value?

- Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 8

What is your conclusion?

- Select your answer -Conclude that the mean time is not the same for all three manufacturersConclude that the mean time is same for all three manufacturersItem 9

Solutions

Expert Solution

Step(1)

Input of the Data in Excel

y Manufacturer 1 Manufacturer 2
17 1 0
23 1 0
21 1 0
19 1 0
29 0 1
27 0 1
32 0 1
28 0 1
17 0 0
16 0 0
20 0 0
19 0 0

Answer(b) The microsoft excel output is given below

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.928399
R Square 0.861925
Adjusted R Square 0.831241
Standard Error 2.211083
Observations 12
ANOVA
df SS MS F Significance F
Regression 2 274.6667 137.3333 28.09091 0.000135
Residual 9 44 4.888889
Total 11 318.6667
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 18 1.105542 16.28161 5.52E-08 15.49909 20.50091 15.49909 20.50091
Manufacturer 1 2 1.563472 1.279204 0.23282 -1.53682 5.536819 -1.53682 5.536819
Manufacturer 2 11 1.563472 7.035624 6.08E-05 7.463181 14.53682 7.463181 14.53682

Therefore the estimated regression equation is

Answer(c)

Answer(d )

Screenshot:


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