A company manufactures printers and fax machines at plants located in Atlanta, Dallas, and Seattle. To measure how much employees at these plants know about quality management, a random sample of 6 employees was selected from each plant and the employees selected were given a quality awareness examination. The examination scores for these 18 employees are shown in the following table. The sample means, sample variances, and sample standard deviations for each group are also provided. Managers want to use these data to test the hypothesis that the mean examination score is the same for all three plants. Plant 1 Plant 2 Plant 3 Atlanta Dallas Seattle 84 72 60 74 74 63 82 74 61 77 75 68 72 68 76 85 81 68 Sample 79 74 66 mean Sample variance 29.6 18.0 35.6 Sample standard deviation 5.44 4.24 5.97

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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A company manufactures printers and fax machines at plants located in Atlanta, Dallas, and Seattle. To measure how much employees at these plants know about quality management, a random sample
of 6 employees was selected from each plant and the employees selected were given a quality awareness examination. The examination scores for these 18 employees are shown in the following table.
The sample means, sample variances, and sample standard deviations for each group are also provided. Managers want to use these data to test the hypothesis that the mean examination score is the
same for all three plants.
Plant 1
Plant 2
Plant 3
Atlanta
Dallas
Seattle
84
72
60
74
74
63
82
74
61
77
75
68
72
68
76
85
81
68
Sample
79
74
66
mean
Sample
variance
29.6
18.0
35.6
Sample
standard
5.44
4.24
5.97
deviation
Set up the ANOVA table for these data. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.)
Source
Sum
Degrees
of Freedom
Mean
F
p-value
of Variation
of Squares
Square
Treatments
Error
Total
Test for any significant difference in the mean examination score for the three plants. Use = 0.05.
Transcribed Image Text:A company manufactures printers and fax machines at plants located in Atlanta, Dallas, and Seattle. To measure how much employees at these plants know about quality management, a random sample of 6 employees was selected from each plant and the employees selected were given a quality awareness examination. The examination scores for these 18 employees are shown in the following table. The sample means, sample variances, and sample standard deviations for each group are also provided. Managers want to use these data to test the hypothesis that the mean examination score is the same for all three plants. Plant 1 Plant 2 Plant 3 Atlanta Dallas Seattle 84 72 60 74 74 63 82 74 61 77 75 68 72 68 76 85 81 68 Sample 79 74 66 mean Sample variance 29.6 18.0 35.6 Sample standard 5.44 4.24 5.97 deviation Set up the ANOVA table for these data. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.) Source Sum Degrees of Freedom Mean F p-value of Variation of Squares Square Treatments Error Total Test for any significant difference in the mean examination score for the three plants. Use = 0.05.
Test for any significant difference in the mean examination score for the three plants. Use a = 0.05.
State the null and alternative hypotheses.
Hoi H1# Hz # H3
Hai H1 = Hz = H3
Ho: Not all the population means are equal.
Hai H1 = H2 = H3
Ho: At least two of the population means are equal.
H: At least two of the population means are different.
Ho: H1 = H2 = H3
Ha: H1# Hz# H3
Ho: H1 = H2 = H3
H: Not all the population means are equal.
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
Do not reject Ho. There is not sufficient evidence to conclude that the means for the three plants are not equal.
Do not reject Ho. There is sufficient evidence to conclude that the means for the three plants are not equal.
Reject Ho. There is sufficient evidence to conclude that the means for the three plants are not equal.
Reject Ho. There is not sufficient evidence to conclude that the means for the three plants are not equal.
Submi+ Ang
O O O O
Transcribed Image Text:Test for any significant difference in the mean examination score for the three plants. Use a = 0.05. State the null and alternative hypotheses. Hoi H1# Hz # H3 Hai H1 = Hz = H3 Ho: Not all the population means are equal. Hai H1 = H2 = H3 Ho: At least two of the population means are equal. H: At least two of the population means are different. Ho: H1 = H2 = H3 Ha: H1# Hz# H3 Ho: H1 = H2 = H3 H: Not all the population means are equal. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Do not reject Ho. There is not sufficient evidence to conclude that the means for the three plants are not equal. Do not reject Ho. There is sufficient evidence to conclude that the means for the three plants are not equal. Reject Ho. There is sufficient evidence to conclude that the means for the three plants are not equal. Reject Ho. There is not sufficient evidence to conclude that the means for the three plants are not equal. Submi+ Ang O O O O
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