Lab Assignment 3 Question 1 A consumer would like to know if there is a difference in the performance

Lab Assignment 3

Question 1

A consumer would like to know if there is a difference in the performance of three different laundry detergents. Eighteen pieces of white cloth were soiled with grape juice then washed in one of the three detergents A, B, or C. The resulting whiteness readings are listed below, where the larger number indicates whiter fabric.

DETERGENT A	DETERGENT B	DETERGENT C
77	73	84
71	68	78
81	66	82
78	74	81
76	70	78
80	60	80

State the null and alternative hypotheses to test the hypothesis of equality of the mean whiteness readings for the three detergents.
How many degrees of freedom are associated with the F test statistic?
Calculate the value of the test statistic F .
Set up the ANOVA Table.
Set up the rejection region for $\alpha $ = 0.05.
What is the appropriate conclusion?
Develop a 95% confidence interval for ${{\mu }_{A}}$.
Develop and interpret a 95% confidence interval for ${{\mu }_{B}}-{{\mu }_{C}}$.

Question 2

A computer laboratory manager must choose between three brands of battery packs for use in a laboratory of laptop computers. A major concern is the time, in hours, the battery packs will function before needing to be recharged. The manager obtains a random sample of eight observations for each of the three brands and records the following information:

	Battery Pack 1	Battery Pack 2	Battery Pack3
	6.9	6.4	6.9
	7.2	6.9	6.3
	7.8	6.1	7.8
	6.3	7.2	7.2
	6.2	7.4	7.8
	6.5	6.1	7.3
	7.0	5.9	7.2
	7.4	6.3	7.5
Total ( ${{T}_{i}}$ )	55.3	52.3	58.0
Mean ( ${{\bar{x}}_{i}}$ )	6.9125	6.5375	7.2500
Standard Deviation ( ${{s}_{i}}$ )	0.5566	0.5579	0.4928

$\sum{\sum{x_{ij}^{2}}}$ = 1150.72, and $\sum{\sum{{{x}_{ij}}}}$ = 165.6

Use Tukey’s method of comparison to determine which of the three battery pack means differ from the others. Let $\alpha $ = 0.05.

Question 3

The data that follow are observations collected from an experiment that compared four treatments, A, B, C, and D, within each of three blocks, using a randomized block design.

Treatment

Block	A	B	C	D
1	7	11	9	10
2	5	10	6	8
3	13	16	15	15

Do the data present sufficient evidence to indicate differences among the treatment means? Test using $\alpha $ = 0.05.
Do the data present sufficient evidence to indicate differences among the block means? Test using $\alpha $ = 0.05.
Find a 95% confidence interval for the difference in means for treatments A and B.

Does it appear that the use of a randomized block design for this experiment was justified? Explain.
Question 4 (Do it by hand and attach a computer printout)
The following data were generated from a 2x2 factorial experiment with 3 replicates, where factor A levels represent two different injection procedures of an anesthetic to the occipital nerve (located in the back of the neck), and factor B levels represent two different drugs, which physicians recommend to increase the effectiveness of the injections. Three headache patients were randomly selected for each combination of injection and drug.
Factor B

Factor A	1	2
1	7	13
	10	11
	8	12
2	10	16
	11	15
	6	11

Test at the 5% significance level to determine if differences exist among the four treatment means.
Test at the 5% significance level to determine if factors A and B interact.
Test at the 5% significance level to determine if differences exist among the levels of factor A .
Test at the 5% significance level to determine if differences exist among the levels of factor B .