Referring back to the process map that I worked in class thatinvolved “getting to work on time”. Suppose that during theconstruction of that process map, we came up with many potentialcauses for why we might be getting to work late. We placed thosecauses 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 afeeling that getting to bed late was causing us to get to worklate. However, we decided to do an experiment. For 8 weeks (5 Daysper week) we tried to go to bed earlier. For these 8 weeks, werecorded our arrival time at work. The following is the arrivaltimes. Note: Our specification for arrival is 8:00 am, which is 480minutes.) Using the same notation, we put the arrival times inminutes. The mean and standard deviation for the 40 arrival timesabove is 447.38 and 11.21, respectively, if you want to work thefollowing two questions by hand.

1) Calculate the 95% confidence interval for the mean arrivaltime using the data above.

2) If our previous average arrival time was 452 minutes, did wesignificantly change the process of getting to work on time? Or inother words, is the arrival time different? Use your confidenceinterval from question 1 to answer this question.

3) If our previous average arrival time was 452 minutes, did wesignificantly change the process of getting to work on time? Or inother words, is the arrival time different? Perform a hypothesistest to answer this question at the 5% level of significance. (Usea t-statistic)