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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