Question

A new operator was recently assigned to a crew of workers who
perform a certain job. From the records of the number of units of
work completed by each worker each day last month, a sample of size
five was randomly selected for each of the two experienced workers
and the new worker. At the *α* = .05 level of significance,
does the evidence provide sufficient reason to reject the claim
that there is no difference in the amount of work done by the three
workers?

Workers | |||

New | A | B | |

Units of work (replicates) | 10 | 11 | 12 |

9 | 13 | 10 | |

8 | 11 | 9 | |

9 | 13 | 13 | |

11 | 12 | 13 |

(a) Find the test statistic. (Give your answer correct to two
decimal places.)

(ii) Find the *p*-value. (Give your answer bounds
exactly.)

< *p* <

(b) State the appropriate conclusion.

Reject the null hypothesis, there is not significant evidence of a difference in units of work between the workers. Reject the null hypothesis, there is significant evidence of a difference in units of work between the workers. Fail to reject the null hypothesis, there is significant evidence of a difference in units of work between the workers. Fail to reject the null hypothesis, there is not significant evidence of a difference in units of work between the workers.

Answer #1

The statistical software output for this problem is:

Hence,

a) Test statistic = **4.96**

b) **0.025 < P < 0.50**

Reject the null hypothesis, there is significant evidence of a difference in units of work between the workers.

A new operator was recently assigned to a crew of workers who
perform a certain job. From the records of the number of units of
work completed by each worker each day last month, a sample of size
five was randomly selected for each of the two experienced workers
and the new worker. At the α = .05 level of significance,
does the evidence provide sufficient reason to reject the claim
that there is no difference in the amount of...

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