Question

A supervisor of a manufacturing plant is interested in relating
the average number of defects produced per day to two factors: the
operator working the machine and the machine itself. The supervisor
randomly assigns each operator to use each machine for three days
and records the number of defects produced per day. Is there
sufficient evidence to conclude that there is a significant
difference among the average number of defects produced per day for
the different machines?

Operator A | Operator B | |
---|---|---|

Machine A | 88 | 44 |

88 | 22 | |

66 | 22 | |

44 | 66 | |

Machine B | 44 | 22 |

88 | 77 | |

88 | 22 | |

44 | 66 | |

Machine C | 00 | 00 |

55 | 77 | |

22 | 00 | |

00 | 11 |

Source of Variation | SSSS | dfdf | MSMS |
---|---|---|---|

Total | 188.0000188.0000 | 2323 | |

Machine | 54.250054.2500 | 22 | 27.125027.1250 |

Operator | 13.500013.5000 | 11 | 13.500013.5000 |

Interaction | 10.750010.7500 | 22 | 5.37505.3750 |

Within | 109.5000109.5000 | 1818 | 6.08336.0833 |

Step 1 of 2:

Find the value of the test statistic for testing the difference among the average number of defects produced per day for the different machines. Round your answer to two decimal places, if necessary.

Step 2 of 2:

Make the decision to reject or fail to reject the null hypothesis of equal average number of defects produced per day for the different machines and state the conclusion in terms of the original problem. Be sure to test for interaction first. Use α=0.05α=0.05.

Answer #1

Source of Variation |
SS |
df |
MS |
F |
P-value |
F crit |

machine | 54.25 | 2 | 27.125 | 4.46 | 0.0267 | 3.55 |

operator | 13.5 | 1 | 13.5 | 2.22 | 0.1536 | 4.41 |

Interaction | 10.75 | 2 | 5.375 | 0.88 | 0.4305 | 3.55 |

Within | 109.5 | 18 | 6.0833 | |||

Total | 188 | 23 |

step 1 of 2"

value of the test statistic for testing the difference among the average number of defects produced per day for the different machines =27.125/6.0833 =4.46

Step 2 of 2:

(Since for interaction :critical value is not less than test statistic , interaction is not significant)

for 0.05 level and (2,18) degree of freedom, critical value =3.55.

since test statistic is higher than critical value. we reject the null hypothesis of equal average number of defects produced per day for the different machines

And conclude that at least one machine has different mean from others,

The following data was collected to explore how the average
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