Quality Management of a Company Worksheet

Description

You may need to use the appropriate technology to answer this question.

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
Atlanta
Plant 2
Dallas
Plant 3
Seattle
867058
747464
837462
767368
726874
899176
Sample
mean
807567
Sample
variance
48.467.249.2
Sample
standard
deviation
6.968.207.01

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
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
Fp-value
Treatments
Error
Total

Test for any significant difference in the mean examination score for the three plants. Use 𝛼 = 0.05.

State the null and alternative hypotheses.

H0: At least two of the population means are equal.
Ha: At least two of the population means are different.H0: 𝜇1 = 𝜇2 = 𝜇3
Ha: Not all the population means are equal. H0: Not all the population means are equal.
Ha: 𝜇1 = 𝜇2 = 𝜇3H0: 𝜇1 ≠ 𝜇2 ≠ 𝜇3
Ha: 𝜇1 = 𝜇2 = 𝜇3H0: 𝜇1 = 𝜇2 = 𝜇3
Ha: 𝜇1 ≠ 𝜇2 ≠ 𝜇3

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.

Reject H0. There is sufficient evidence to conclude that the means for the three plants are not equal.Do not reject H0. There is sufficient evidence to conclude that the means for the three plants are not equal. Reject H0. There is not sufficient evidence to conclude that the means for the three plants are not equal.Do not reject H0. There is not sufficient evidence to conclude that the means for the three plants are not equal.You may need to use the appropriate technology to answer this question.

The following data are from a completely randomized design. In the following calculations, use 𝛼 = 0.05.

Treatment
1
Treatment
2
Treatment
3
638370
467155
548761
376750
xj507759
sj2123.3390.6774.00

(a)

Use analysis of variance to test for a significant difference among the means of the three treatments.

State the null and alternative hypotheses.

H0: Not all the population means are equal.
Ha: 𝜇1 = 𝜇2 = 𝜇3H0: At least two of the population means are equal.
Ha: At least two of the population means are different. H0: 𝜇1 = 𝜇2 = 𝜇3
Ha: 𝜇1 ≠ 𝜇2 ≠ 𝜇3H0: 𝜇1 = 𝜇2 = 𝜇3
Ha: Not all the population means are equal.H0: 𝜇1 ≠ 𝜇2 ≠ 𝜇3
Ha: 𝜇1 = 𝜇2 = 𝜇3

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 = 

State your conclusion.

Do not reject H0. There is sufficient evidence to conclude that the means of the three treatments are not equal.Do not reject H0. There is not sufficient evidence to conclude that the means of the three treatments are not equal. Reject H0. There is not sufficient evidence to conclude that the means of the three treatments are not equal.Reject H0. There is sufficient evidence to conclude that the means of the three treatments are not equal.

(b)

Use Fisher’s LSD procedure to determine which means are different.

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

LSD = 

Find the pairwise absolute difference between sample means for each pair of treatments.

x1 − x2

x1 − x3

x2 − x3

Which treatment means differ significantly? (Select all that apply.)

There is a significant difference between the means for treatments 1 and 2.There is a significant difference between the means for treatments 1 and 3.There is a significant difference between the means for treatments 2 and 3.There are no significant differences.

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