Question

Consider the experimental results for the following randomized block design. Make the calculations necessary to set up the analysis of variance table.

		Treatments
		A	B	C
Blocks	1	9	9	8
	2	12	6	5
	3	18	15	14
	4	20	18	18
	5	8	7	8

Use α = 0.05 to test for any significant differences.

Find the value of the test statistic. (Round your answer to two decimal places.)___

Find the p-value. (Round your answer to three decimal places.)

p-value = ___

The following data were obtained for a randomized block design involving five treatments and three blocks: SST = 570, SSTR = 390, SSBL = 95. Set up the ANOVA table. (Round your value for F to two decimal places, and your p-value to three decimal places.)

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Treatments	390
Blocks	95
Error	85
Total	570

Test for any significant differences. Use α = 0.05.

Find the value of the test statistic. (Round your answer to two decimal places.)____

Find the p-value. (Round your answer to three decimal places.)

p-value = ____

An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tune-up time varies among compact, intermediate, and full-sized cars, the three types of cars were used as blocks in the experiment. The data obtained follow.

		Analyzer
		Computerized	Electronic
Car	Compact	51	43
	Intermediate	55	44
	Full-sized	62	45

Use α = 0.05 to test for any significant differences.

Find the value of the test statistic. (Round your answer to two decimal places.)____

Find the p-value. (Round your answer to three decimal places.)

p-value = ____

Answer 1

1. From the given data

ANOVA Table
Source	df	Sum of square	mean Square	F	F-critical	P-value
Treatment	2	390	195	18.35	4.4590	0.001
Block	4	95	23.75	2.24	3.8379	0.155
Error	8	85	10.625
Total	14	570

Use α = 0.05 to test for any significant differences.

Find the value of the test statistic. (Round your answer to two decimal places.)

For Treatment: F = 18.35

For Block : F = 2.24

Find the p-value. (Round your answer to three decimal places.)

p-value = 0.001 for treatment

P-value = 0.155 for block

Since P-value = 0.001 < alpha 0.05 so we reject H0

Thus we conclude that there is significant difference among the treatments

and

Since P-value = 0.155 >< alpha 0.05 so we do not reject H0

Thus we conclude that there is not significant difference among the blocks

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2. H0: Car and Analyzer are independent

H1: Car and Analyzer are not independent

Let the los be alpha = 5%

The observed frequencies are

	Computerized	Electronic	Total
Compact	51	43	94
Intermediate	55	44	99
Full-sized	62	45	107
Total	168	132	300

The expected frequencies are

	Computerized	Electronic	Total
Compact	52.64	41.36	94
Intermediate	55.44	43.56	99
Full-sized	59.92	47.08	107
Total	168	132	300

The chi-square contribution values are

Oi	Ei	(Oi-Ei)^2 /Ei
51	52.64	0.0511
43	41.36	0.065
55	55.44	0.0035
44	43.56	0.0044
62	59.92	0.0722
45	47.08	0.0919
	Total:	0.2881

Degrees of freedom: 2

Test Statistic, X^2: 0.29

P-Value: 0.866

since P-value > alpha 0.05 so we accept H0

Thus we conclude that Car and Analyzer are independent