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