# 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 | |
---|---|---|---|

86 | 70 | 58 | |

74 | 74 | 64 | |

83 | 74 | 62 | |

76 | 73 | 68 | |

72 | 68 | 74 | |

89 | 91 | 76 | |

Sample mean | 80 | 75 | 67 |

Sample variance | 48.4 | 67.2 | 49.2 |

Sample standard deviation | 6.96 | 8.20 | 7.01 |

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 | F | p-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.

*H*_{0}: At least two of the population means are equal.*H*_{a}: At least two of the population means are different.*H*_{0}: 𝜇_{1} = 𝜇_{2} = 𝜇_{3}*H*_{a}: Not all the population means are equal. *H*_{0}: Not all the population means are equal.*H*_{a}: 𝜇_{1} = 𝜇_{2} = 𝜇_{3}*H*_{0}: 𝜇_{1} ≠ 𝜇_{2} ≠ 𝜇_{3}*H*_{a}: 𝜇_{1} = 𝜇_{2} = 𝜇_{3}*H*_{0}: 𝜇_{1} = 𝜇_{2} = 𝜇_{3}*H*_{a}: 𝜇_{1} ≠ 𝜇_{2} ≠ 𝜇_{3}

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 *H*_{0}. There is sufficient evidence to conclude that the means for the three plants are not equal.Do not reject *H*_{0}. There is sufficient evidence to conclude that the means for the three plants are not equal. Reject *H*_{0}. There is not sufficient evidence to conclude that the means for the three plants are not equal.Do not reject *H*_{0}. 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 | |
---|---|---|---|

63 | 83 | 70 | |

46 | 71 | 55 | |

54 | 87 | 61 | |

37 | 67 | 50 | |

x_{j} | 50 | 77 | 59 |

s_{j}^{2} | 123.33 | 90.67 | 74.00 |

(a)

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

State the null and alternative hypotheses.

*H*_{0}: Not all the population means are equal.*H*_{a}: 𝜇_{1} = 𝜇_{2} = 𝜇_{3}*H*_{0}: At least two of the population means are equal.*H*_{a}: At least two of the population means are different. *H*_{0}: 𝜇_{1} = 𝜇_{2} = 𝜇_{3}*H*_{a}: 𝜇_{1} ≠ 𝜇_{2} ≠ 𝜇_{3}*H*_{0}: 𝜇_{1} = 𝜇_{2} = 𝜇_{3}*H*_{a}: Not all the population means are equal.*H*_{0}: 𝜇_{1} ≠ 𝜇_{2} ≠ 𝜇_{3}*H*_{a}: 𝜇_{1} = 𝜇_{2} = 𝜇_{3}

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 *H*_{0}. There is sufficient evidence to conclude that the means of the three treatments are not equal.Do not reject *H*_{0}. There is not sufficient evidence to conclude that the means of the three treatments are not equal. Reject *H*_{0}. There is not sufficient evidence to conclude that the means of the three treatments are not equal.Reject *H*_{0}. 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.

*x*_{1} − *x*_{2}

=

*x*_{1} − *x*_{3}

=

*x*_{2} − *x*_{3}

=

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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