A production engineer claims that there is no difference in the mean nut

diameter manufactured by two different methods. The first method produces nuts with the following diameters (in centimeters).

3.33 |
3.337 |
3.329 |
3.354 |
3.325 |
3.343 |
3.333 |
3.347 |
3.332 |
3.358 |

3.353 |
3.335 |
3.341 |
3.331 |
3.327 |
3.326 |
3.337 |
3.336 |
3.323 |
3.347 |

3.329 |
3.345 |
3.329 |
3.338 |
3.353 |
3.339 |
3.338 |
3.338 |
3.35 |
3.32 |

3.364 |
3.34 |
3.348 |
3.339 |
3.336 |
3.321 |
3.316 |
3.352 |
3.32 |
3.336 |

The second method produces nuts with theses diameters (in centimeters).

Use an alpha level of .01 and test the hypothesis that the two methods are producing the same mean.

**Solution: **We have to use a (non-paired) t-test. First we analyze the variances with an F-test. The outcome from EXCEL is:

The p-value=2*0.315658=0.631 indicates that the difference is not significant, and we can assume equal variances.

Now we run a t-test (assuming equal variances). The EXCEL output follows:

The p-value is 1.59396E-70, which is less than 0.01. That means that *we reject the null hypothesis that the **two methods are producing the same mean, at the 0.01 level of significance*.

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