【正文】 m2 649 Six Sigma Example ? Suppose the manager believes that spending less time on the phone is preferable ? He suspects that new employees are spending more time on the phone than experienced employees, and collects data to learn whether this is the case ? Hypotheses are now: ? H0: ?mnew ≤ ?mexperienced ? Ha: ?mnew ?mexperienced 650 Six Sigma OneSided Hypothesis Testing 651 Six Sigma Comparisons involving X with 2 levels Comparisons involving X with 3 or more levels Comparisons to a specific value (an X with 1 level) Example Bob against a standard Example Bob Jane against each other Example Bob, Jane, and Walt against each other Analyze Roadmap 652 Six Sigma Example – 1 Level of X ? A customer service center manager estimated that the average time Bob spends on a telephone call with a customer is 5 minutes. Is this correct? ? This is an example of a hypothesis test that pares one sample with a belief. ? H0: m = 5 ? Ha: m ≠ 5 ? The manager collected data on 20 calls. Would it matter whether the 20 calls were from the same day as opposed to one call on each of 20 days? Call Time 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Ave Std dev Project: GB Worksheet: Call Length 653 Six Sigma 1sample Wilcoxon test of median 1sample ttest of mean Minitab What to look for or ask Comparisons Involving X with 1 Level Study Stability (if applicable) Study Shape Study Centering SPC Chart IMR Is the data stable over time? Look for any trends or patterns. 1Sample test Normal NonNormal Small PValue (.05) ? Mean (or Median) not equal to hypothesized value Analyze Roadmap – 1 Sample Descriptive Stats, Normal Probability Plot Points should fall on a straight line on the normal probability plot. ttests will still work as long as the data is not badly skewed. Graphical Analysis Boxplot, dotplot, histogram, etc. Provides a picture of the data. Does the signal look large relative to the noise? 654 Six Sigma Minitab?s 1sample ttest 655 Six Sigma ttest: Minitab?s Numerical Output OneSample T: Time Test of mu = 5 vs mu not = 5 Variable N Mean StDev SE Mean Time 20 Variable % CI T P Time ( , ) tstatistic – SignaltoNoise ratio pvalue – there is a % chance that our results could have been produced by a population with a mean of 5. 656 Six Sigma 5 . 55 . 04 . 54 . 0T i m eB o x p l o t o f T i m e( w i t h H o a n d 9 5 % t c o n f i d e n c e i n t e r v a l f o r t h e m e a n )[ ]X_H oBoxplot with Confidence Interval The red line shows the confidence interval for the mean. The blue dot is the hypothesized value. Note that while we?re quite confident the mean is not 5, individual calls may be as long as or longer than 5 minutes. 657 Six Sigma Example: Conclusions ? The pvalue is the probability of observing a signal as large as ours (or larger) if H0 is true ? In our example, there is a % probability of observing a signal as large as if the mean is really 5. ? Since the pvalue is so small, the result is considered statistically significant ? The actual difference is about 15 seconds. Whether this is of practical importance can only be determined by the people involved in the process 658 Six Sigma 謝謝觀看 /歡迎下載 BY FAITH I MEAN A VISION OF GOOD ONE CHERISHES AND THE ENTHUSIASM THAT PUSHES ONE TO SEEK ITS FULFILLMENT REGARDLESS OF OBSTACLES. BY FAITH I BY FAIT