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

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Presentation transcript:

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

| 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 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.

| 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 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.

| 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 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?

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

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

| 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 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?

| 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | 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.

| 9.2 | 9.3 | 9.4 | 9.5 | 9.6 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | Confidence Interval -- continued n The difference between sample means is hours, the pooled estimate of the common population standard deviation is hours, the standard error of the sample mean difference is hours; these values lead to the following 95% confidence interval for the mean difference: to 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.