Assignment
1) An experiment was conducted to determine the effect of pressure and temperature on the performance of a chemical substance. We used two levels of pressure (in pounds per square inch, psi) and three temperatures:
|
Pressure(psi)
|
Temperature (F)
|
|
50
|
100
|
|
80
|
200
|
|
300
|
A test of experiment on each combination of temperature resulted in the data listed in the following table:
|
Performance
|
Pressure (psi)
|
Temperature (F)
|
|
21
|
50
|
100
|
|
23
|
50
|
200
|
|
26
|
50
|
300
|
|
22
|
80
|
100
|
|
23
|
80
|
200
|
|
28
|
80
|
300
|
State the hypothesis.
Find the regression equation
What is the value of R2? What does imply?
There is a statistically significant relationship between which ones?
What information does the ANOVA table give us?
2) An experiment with different types of boxes were compared in terms of the force of compressed we expected to find significant differences between the averages of tablet of the different types of boxes. (Α = 0.05).
Make a "Box Plot" Comparative
Normality probability plot
Do a statistical test; if you find significant differences use the Tukey method
Determine the power of test
3) Three different varieties of tomatoes (Hunester (H), Pusa (P) and Ife No. 1 (If1)) and four different densities of plantations (10, 20, 30 and 40 thousand plants per hectare) are being considered to be planted in a certain region. To see if the variety or the plant density affect the product, each combination of variety and density are used in three "plots" different, results in the production data then. "(Α = 0.01)
|
Type of box
|
Power of Compression
|
|
1
|
655.5
|
788.3
|
734.3
|
721.4
|
679.1
|
699.4
|
|
2
|
789.2
|
772.5
|
786.9
|
686.1
|
732.1
|
774.8
|
|
3
|
737.1
|
639.0
|
696.3
|
671.7
|
717.2
|
727.1
|
|
4
|
535.1
|
628.7
|
592.4
|
559.0
|
586.9
|
520.0
|
|
Variety
|
PlantationDensity
|
|
10,000
|
20,000
|
30,000
|
40,000
|
|
H
|
10.5, 9.2, 7.9
|
12.8, 11.2, 13.3
|
12.1, 12.6, 14.0
|
10.8, 9.1, 12.5
|
|
If1
|
8.1, 8.6, 10.1
|
12.7, 13.7, 11.5
|
14.4, 15.4, 13.7
|
11.3, 12.5, 14.5
|
|
P
|
16.1, 15.3, 17.5
|
16.6, 19.2, 18.5
|
20.8, 18.0, 21.0
|
18.4, 18.9, 17.3
|
Test the hypothesis.
Use Tukey to test if the interaction hypothesis is not rejected, and at least one of the major effects in terms of the null is rejected.
4) A company packs a product in three different sizes of canning. Many of the cans are in conformity with the specifications. A quality control engineer has identified the following reasons for dissatisfaction by in customer: a sample is selected in terms of units comprising three lines quality and each unit is categorized agree because of non-conformity. The data below:
|
Line of Production
|
Reasons for Inconformity
|
|
Stain on the can
|
Broken
|
Pull tab misplaced
|
Pull tab missing
|
Others
|
|
1
|
34
|
65
|
17
|
21
|
13
|
|
2
|
23
|
52
|
25
|
19
|
6
|
|
3
|
32
|
28
|
16
|
14
|
10
|
The data suggests that the proportions that fall into different categories of non-conformity are different for all three lines for α = 0.05.
5) Three different brands of magnetron tubes (key components in microwave ovens) were subjected to stress tests registering the number of hours that each of them operated without need of repair (see table). Although these times do not represent typical service life times, it indicates how well these tubes withstand extreme strain.
Prove that the duration medium effort is the same for all three brands. What are the necessary assumptions in order to validate this procedure?
Using an adequate test, determine if there is evidence to conclude that the magnetron tube brands tend to differ in duration with effort using an α.
|
Brand A
|
Brand B
|
Brand C
|
|
36
|
49
|
71
|
|
48
|
33
|
31
|
|
5
|
60
|
140
|
|
67
|
2
|
59
|
|
53
|
55
|
42
|