1. Example 9.7 Reliability of Treadmill Motors at the SureStep Company Confidence Interval for the Difference Between Means

2. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.89.99.109.119.129.139.149.15 Objective To use StatPro’s two-sample procedure to find a confidence interval for the difference between mean lifetimes of motors, and to see how this confidence interval can help SureStep choose the better supplier.

3. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.89.99.109.119.129.139.149.15 Background Information n The SureStep Company manufactures high-quality treadmills for use in exercise clubs. n SureSteps currently purchases its motors for these treadmills from supplier A. n However, it is considering a change to supplier B, which offers a slightly lower cost. The only question is whether supplier B’s motors are as reliable as supplier A’s.

4. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.89.99.109.119.129.139.149.15 Background Information -- continued n To check this SureStep installs motors from supplier A on 30 of its treadmills and motors from supplier B on another 30 of its treadmills. n It then runs these treadmills under typical conditions and, for each treadmill, records the number of hours until the motor fails. n What can SureStep conclude?

5. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.89.99.109.119.129.139.149.15 MOTORS.XLS n The data from the experiment appears in this file. Here is a portion of that data.

6. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.89.99.109.119.129.139.149.15 Boxplots n In any comparison problem it is a good idea to look initially at side-by-side boxplots of the two samples.

7. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.89.99.109.119.129.139.149.15 Boxplots -- continued n The boxplots show –the distribution of times until failure are skewed to the right for each supplier –the mean for supplier A is somewhat greater than the mean for supplier B –there are several mild outliers n There seems to be little doubt that supplier A’s motors will last longer on average than supplier B’s - or is there?

8. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.89.99.109.119.129.139.149.15 Confidence Interval n A confidence interval for the mean difference allows us to see whether the differences apparent in the boxplots can be generalized to all motors from the two suppliers. n We find this confidence interval by using StatPro Two-Sample procedure. n It shows that the sample means differ by approximately 93 hours and that the sample standard deviations are of roughly the same magnitude.

9. 9.19.1 | 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 9.159.29.39.49.59.69.89.99.109.119.129.139.149.15 Confidence Interval -- continued n The difference between sample means is 93.133 hours, the pooled estimate of the common population standard deviation is 272.196 hours, the standard error of the sample mean difference is 70.281 hours; these values lead to the following 95% confidence interval for the mean difference: 47.549 to 233.815. n Not only is this interval wide but it ranges from a negative value to a positive value. n If SureStep has to guess they would say that supplier A’s motors lasted longer, but because of the negative number there is still a possibility that the opposite is true.