Assignment

1. (
2 points
) The ANOVA from a randomized complete block experiment output is shown below.

Source	DF	SS Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper	MS	F	P
Treatment		4	10 10. 5 6	252.64	2 9 .84	3 .54489E-08
Block	?	323.82	64. 7 65	7.649	0.00036885
Error	20	169.33	8.4467
Total	29	15 03.71

a. Fill in the blanks.  You may give bounds on the P-value.

b. How many blocks were used in this experiment?

c. What conclusions can you draw?

0. (
3 points
) An aluminum master alloy manufacturer produces grain refiners in ingot form.  The company produces the product in four furnaces.  Each furnace is known to have its own unique operating characteristics, so any experiment run in the foundry that involves more than one furnace will consider furnaces as a nuisance variable.  The process engineers suspect that stirring rate impacts the grain size of the product.  Each furnace can be run at four different stirring rates.  A randomized block design is run for a particular refiner and the resulting grain size data is as follows.

5

6

7

10

15

7

10

3

10

4

7

Stirring Rate	Furnace
1	2		3	4
	5	9		6				7
			10		15
15
20	18

a. Is there any evidence that stirring rate impacts grain size?

b. What should the process engineers recommend concerning the choice of stirring rate and furnace for this particular grain refiner if small grain size is desirable? 

1

. (

2

.5 points) A biochemist is interested in the effects of two different catalysts and two different temperatures on the rate of a chemical reaction.  She performs six replicates of a 22 design, making the runs in random order.  Analyze the rate of chemical reaction data that follow and draw appropriate conclusions.  

35

36

48

49

45

Catalyst
Temperature			1			2
3 1	32		35		36
350 K	33	38	34
30	39	37
47		49	41	44
360 K		48	43
	45	46	40

(2.5 points)
An engineer suspects that the surface finish of a metal part is influenced by the feed rate and the depth of cut.  She selects three feed rates and four depths of cut.  She then conducts a factorial experiment and obtains the following data:

0.20

97

104

109

0.25

109

93

93

104

104

109

113

103

104

115

100

104

Depth of Cut (in)
Feed Rate (in/min)	0.15	0.18		0.20		0.25
79	84	87						104
69	73			93				109
65	78		97	101
	103
91		113		115
	100
119
0.30	116
107	112

a. Analyze the data and conclusions.  Use  = 0.05.

3.  (2.5 points) the effect of three different grades of gasoline on fuel economy in car engines is being studied.  Fuel economy is measured using brake-specific fuel consumption after the engine has been running for 15 minutes.  Five different car engines are available for the study, and the experimenters conduct the following randomized complete block design.

1

2

1

2

3

Car
Gasoline grade		3	4	5
0.545	0.685	0.530	0.445	0.550
0.510	0.644	0.497	0.339	0.522
0.523	0.605	0.498	0.410	0.520

(a) Analyze the data from this experiment.

 (b) Use the Bonferroni correction method to make comparisons among the three grades of gasoline to determine specifically which grades differ in brake-specific fuel consumption.

4.  (2.5 points) suppose that we are testing H0: µ = µ0 versus H1: µ ≠ µ0.  Calculate the P-value for the following observed values of the test statistic:

(a) Z0 = 4.9

(b) Z0 = -3  

(c) Z0 = 4.3

(d) Z0 = 3.9

(e) Z0 = -0.5