Referring back to the process map that I worked in class that involved getting to work on time. Suppose that during the construction of that process map, we came up with many potential causes for why we might be getting to work late. We placed those causes in a FMEA and one of the causes that had a high RPN was getting to bed too late. Up until that point, it was just a feeling that getting to bed late was causing us to get to work late. However, we decided to do an experiment. For 8 weeks (5 Days per week) we tried to go to bed earlier. For these 8 weeks, we recorded our arrival time at work. The following is the arrival times. Note: Our specification for arrival is 8:00 am, which is 480 minutes.) Using the same notation, we put the arrival times in minutes.

436	460	442	440	460
445	451	457	459	455
470	432	457	440	456
433	445	452	466	429
453	434	437	453	468
432	458	444	453	438
449	448	440	465	461
448	454	439	425	459

The mean and standard deviation for the 40 arrival times above is 448.57 and 11.58, respectively, if you want to work the following two questions by hand.

• Calculate the 95% confidence interval for the mean arrival time using the data above.
• If our previous average arrival time was 452 minutes, did we significantly change the process of getting to work on time? Or in other words, is the arrival time different? Use your confidence interval from question 1 to answer this question.
• If our previous average arrival time was 452 minutes, did we significantly change the process of getting to work on time? Or in other words, is the arrival time different? Perform a hypothesis test to answer this question at the 5% level of significance. (Use a t-statistic)