## Related questions with answers

National Paper Company must purchase a new machine for producing cardboard boxes. The company must choose between two machines. The machines produce boxes of equal quality, so the company will choose the machine that produces (on average) the most boxes. It is known that there are substantial differences in the abilities of the company's machine operators. Therefore, National Paper has decided to compare the machines using a paired difference experiment. Suppose that eight randomly selected machine operators produce boxes for one hour using machine 1 and for one hour using machine 2, with the following results: Ds BoxYield

Machine Operator | ||||
---|---|---|---|---|

1 | 2 | 3 | 4 | |

Machine 1 | 53 | 60 | 58 | 48 |

Machine 2 | 50 | 55 | 56 | 44 |

Machine Operator | ||||

5 | 6 | 7 | 8 | |

Machine 1 | 46 | 54 | 62 | 49 |

Machine 2 | 45 | 50 | 57 | 47 |

Assuming normality, perform a hypothesis test to determine whether there is a difference between the mean hourly outputs of the two machines. Use $\alpha=.05$

Solutions

VerifiedThe goal of the exercise is to perform a hypothesis test to determine whether there is a difference between the mean hourly outputs of the two machines under the normally distributed. Use $\alpha=0.05$.

The goal of this task is to set the null and the alternative hypothesis. The hypotheses that will help us try to determine is there a difference between the two machines' mean hourly results, is this a null hypothesis

$H_0: \mu_1-\mu_2 = 0,$

and this alternative hypothesis:

$H_a: \mu_1-\mu_2 \neq 0.$

Here $\mu_1$ represents the mean of hourly results for the first machine and $\mu_2$ the mean of hourly results but for the second machine. Also, the hypotheses we set, we have to test them when the value of $\alpha$ is $0.05.$

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