## 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 |

Estimate the minimum and maximum differences between the mean outputs of the two machines. Justify your answer.

Solution

VerifiedIt is required of us to determine the interval for the mean of a population of paired differences with a certain percent of confidence and based on that interval estimate the minimum and maximum difference between the two means. In this case, we have to use this formula which will help us to determine a $100(1-\alpha)\%$ confidence interval for the mean of a population of paired differences and that formula is:

$\left[ \=d \pm t_{\alpha/2}\frac{s_d}{\sqrt{n}} \right].$

Here $\=d$ represents the value of the difference between two sample means, and $s_d$ represents the value of a sample standard deviation. The value of $n$ will tell us how large the sample size is. Also, what is important to know is that the value of $t_{\alpha/2}$ depends on $(n-1)$ degrees of freedom.

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