Management is interested in increasing the efficiency of processing purchase orders. The time to process purchase orders, in days, was observed for 31 randomly selected customers and is shown in given Table. Following a detailed study of the process, certain recommendations were adopted. Twenty-six customers were randomly selected and their purchase order processing times are shown after the process improvement changes.
(a) Find the mean, standard deviation, skew ness coefficient, kurtosis coefficient, and interquartile range of the processing time prior to process changes and comment on the values.
(b) Find the mean, standard deviation, skew ness coefficient, kurtosis coefficient, and interquartile range of the processing time after the process changes and comment on the values.
(c) Find a 95% confidence interval for the mean processing time prior to process changes.
(d) Can we conclude that the mean processing time, before the process changes, is less than 10.5 days? Use α = 0.02. What is the p-value? If α = 0.10, what is your decision? What does this imply?
(e) Can we conclude that the mean processing time, after the process changes, is less than 8.5 days? Use α = 0.05. What is the p-value? Explain.
(f) Is there a difference in the variabilities of processing times before and after process changes? Use α = 0.05.
(g) Can we conclude that the process changes have been effective in reducing the mean processing time? Use α = 0.05. What assumptions do you need to make for conducting the test?