Consider the following situation: Electrical engineers have adevice that tests for battery life (in minutes) by placing abattery under a controlled electrical load and measuring how longit lasts. They are interested in comparing the performance of 4brands of batteries. They replicated the experiment 4 times byrandomly assigning a battery brand to be used in the electricalload device each time they measured battery life. In other words,they made 16 ‘runs’ and randomized the order in which the batterybrands were used.
The data they obtained was:
BrandA | BrandB | BrandC | BrandD |
110 | 118 | 108 | 117 |
113 | 116 | 107 | 112 |
108 | 112 | 112 | 115 |
115 | 117 | 108 | 119 |
1. State the Null and Alternative Hypothesis in words (bothhypotheses) and using statistical notation (null hypothesisonly).
2. Compute the means and sample standard errors for the brands.Upload the file. This can be an Excel spreadsheet, aphoto/screenshot/scanned image.
3. Compute the sums of squares for Treatment, Error, and Total,and complete the ANOVA table below. For each SS, MS, and Fcalculation round to nearest whole number. For example, calculateSS > round to nearest whole number. Use that SS to calculate MS> round to nearest whole number. Use that MS to calculate F >round to nearest whole number.
| Source | DF | SS | MS | F |
| Treatment | | | | |
| Error | | | | |
| Total | | | |
4. Using the F - table and your ANOVA table results, what is thecritical F-value for a test of the hypothesis at the 5% level ofsignificance?
5. Based on your F-test statistic and F-critical value, write acomplete conclusion of your hypothesis test.
6. What is the value from the Tukey table you will used tocalculate the Tukey comparisons?
7. Construct mean comparisons using the Tukey method and uploadyour results. Be sure to provide the Tukey W value (i.e. the valueyou calculated by which you compared the treatment means) and theletter grouping for each of the treatment means. Based on theseTukey comparisons, what battery brand(s) would you conclude differin mean lifetime? This upload can be, for example, a photo taken ofyour work and an upload of that image.
8. Now use Minitab to conduct this analysis. Upload an image ofyour your Minitab output that shows your ANOVA table and groupinginformation of Tukey mean comparisons.
