Poindexter LeMans sat at his Louis XIV desk and looked at the garage monitor. Sure enough, there was his Bugatti Chiron Sport 110 Ans parked snuggly in the middle of his other 50 cars. He thought to himself, Sure $4,000,000 is lot to spend on one car, but how else am I going to get to work on time when my sea-side palatial home is almost 20 miles from the office and I only have 6 free minutes a day to make the trip? He felt that the expense was clearly justified. As you might have guessed Poindexter had a very successful career going or else he wouldnt have had such expensive trappings, and probably would have been fired for goofing off. And youd have guessed right...he was rich. In fact, he never bought a lottery ticket because he was afraid he might win, and he was running out of places to put the money he already had. And he owed all his wealth to rats ... dirty disease-spreading slimy rats. Poindexter had always enjoyed killing rats ever since he used to beat their brains out with a Stanley 54-716 jacketed graphite ball-peen hammer at the orphanage. The Jesuit Priests who ran the place taught him to take pride in his work, and to always use the best tool for the job. They had given him the hammer on his 6th birthday and he couldnt have been happier; he killed 52 rats in the first 24 hours (still a record for a 6-year-old orphan). By the time he was 18 years old environmentalists feared that rats were on the verge of becoming extinct. Fortunately (for the rats) he took several years off to get a college education. After earning his Ph.D. in astrophysics at Cal Tech, he began recklessly experimenting with a new rocket fuel with which he hoped to take a trip to Mars with a few friends (a sort of graduation road trip). But instead he accidentally discovered that rats could be flash frozen with liquid oxygen (LOX). Although the accident caused the tragic loss of a dedicated and hard-working lab rat he had named Stanley (the only rat Poindexter ever loved...named after his hammer), it yielded a clean method of killing rats. This flash freezing of rats avoided the problem in rat extermination. The old way of killing rats, was to put out poison. But, no matter how lethal and fast-acting the poison might be if a big enough rat ate it, it would still have just enough time to crawl in agony back to its home in the wall before dying. The unlucky rat would then slowly decompose causing a horrific stench that would last for months as its inaccessible decaying carcass turned slowly into guacamole. With Poindexters Rat-Freeze trap, even a giant cat-sized rat couldnt move more than an inch before it was frozen as solid as a popsicle at the North Pole in January (or at the South Pole in July). Poindexters advertising proudly proclaimed, The rat will move less than an inch or Ill give you your money back and eat the rat!But now Poindexter was worried. Recently one especially gigantic rat had moved just over two inches before meeting its frosty demise. Poindexter refunded the customers money and ate the rat, as promised in his advertising, but his private chef had

prepared it in a nice barnaise sauce, so it wasnt too bad...the smaller bones were a little crunchy, but not bad otherwise...no more disgusting than Buffalo Wings in any case. Poindexters real fear was that this failure might not be isolated. If another rat was able to move more than an inch, the news would quickly spread, and sales of his trap would surely suffer; his customers, like himself, demanded exactly what was promised: an inch rat movement maximum. Furthermore, although the rat he ate had been tolerable, he didnt really want to eat more than one rat every other week. Finally, Poindexter desperately needed the cash from his rat-freeze sales to buy a villa he had his eye on in Monte-Carlo, and the Gulfstream G650ER he purchased last May caused him to be thoroughly embarrassed whenever one of his billionaire friends saw him flying around in a jet that was almost a full year old. Poindexter thought the traps failure might have something to do with quality problems at the new supplier of his LOX spray nozzles. Specifically, he suspected that the supplier was not properly holding a key diameter at the throat of that nozzle. Poindexter had two types of data available to work with in exploring this problem. The first dataset consisted of 50 individual nozzle diameters. Those diameters are normally distributed and can be found on the first sheet in the Excel file (the sheet labeled 50 Throat Diameters). Poindexters specification on that diameter was 0.1000 plus or minus 0.0050. You may assume that this data was obtained at a time when the process was definitely under control, and (as just stated) known with certainty to be normally distributed.The second dataset (on the second page in the Excel file labeled 20 Samples of Size 5) consists of 20 samples of 5 nozzle throat diameters. This data was taken more recently and perhaps after a problem had developed at the supplier. Each horizontal row represents one sample. Each row first gives the five observations that make up the sample (in columns B to F), then gives the samples mean (in column H) and the samples range (in column I). The 20 samples are listed in the order in which they were taken. That is, sample 1 (the first row) was taken first, sample 2 (the second row) was taken second, etc. Again, this data was taken after a problem may have developed so we dont know if the process was under control or normally distributed.Assume that there is nothing wrong with the design of the Rat Freeze. That is, if the Rat Freeze is manufactured to specification, the rat will freeze on the spot. That means, that either the rat was able to move more than an inch due to a failure in the suppliers process or there really isnt a problem at all (the fact that the rat didnt die instantly was just a very unlikely fluke). You need to find out what the truth is; is there a problem with the suppliers process or not?

Question 1: As you know, a process can have one of two types of problems. It can be out of control or (if it is under control) it still may not be good enough. Which data set should be used to see if the problem is out of control?

Question 2: Do some analysis to decide whether or not the process is under control. Make sure to use the right dataset...you need to decide which to use.

Question 3: Do some analysis to decide if the process is good enough when it is operating normally. Again, use the right dataset.

Question 4: In answering either question 2 or 3, the conclusion you would give after doing the math might change if you draw a graph. Which of the two answers might change if you draw a graph rather than just crunch the numbers? Why?

Question 5: If there is a problem, state what it is and say what Poindexter should do to deal with it. Make sure your answer fits your analysis.In answering questions 2 and 3 make your conclusion clear. For example, for question 2, clearly state if the process is or is not under control.

Item 1 2 3 4 5 7 8 9 10 11 12 13 14 15 16 18 19 20 21 22 23 24 25 26 27 2B 29 30 Throat Diameters 0.1011 0.1011 0.0999 0.1009 0.1008 0.0997 0.1028 0.0991 0.0989 0.1001 0.0996 0.0996 0.1026 0.1016 0.1020 0.1027 0.1012 0.1005 0.1006 0.1010 0.1037 0.1011 0.1013 0.0989 0.1024 0.1026 0.1004 0.1007 0.1021 0.1013 0.0998 0.0991 0.1016 0.1012 0.0992 0.1004 0.1021 0.1023 0.1002 0.1021 0.0982 0.1007 0.1002 0.1011 0.1008 0.1014 0.0997 0.1020 0.1025 0.0997 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Mean Sample 1 2 3 4 5 6 7 8 9 10 11 0.0982 0.0997 0.0998 0.0998 0.0982 0.1028 0.1011 0.1011 0.1026 0.1014 0.0996 0.0996 0.1027 0.1012 0.1014 0.1011 0.1026 0.1004 0.1037 0.1004 Above 0.0989 0.1028 0.1001 0.0991 0.1007 0.0989 0.1011 0.1006 0.1008 0.0997 0.0996 0.1021 0.1012 0.1012 0.1016 0.1002 0.1004 0.1021 0.1011 0.1009 0.1010 0.0991 0.1025 0.1016 0.1002 0.1008 0.0999 0.1013 0.1011 0.1020 0.1026 0.1021 0.1005 0.1008 0.1015 0.0997 0.1007 0.1017 0.1013 0.1020 0.0993 0.0980 0.0991 0.1012 0.1000 0.0997 0.1009 0.1011 0.1004 0.1025 0.1010 0.0996 0.1006 0.1015 0.1000 0.1030 0.1021 0.1002 0.0989 0.1021 0.1005 0.1001 0.0991 0.0992 0.1008 0.1016 0.1008 0.1007 0.0999 0.0997 0.1020 0.1023 0.1010 0.1002 0.1010 0.0996 0.0999 0.1001 0.1002 0.1000 0.1007 0.1008 0.1009 0.1010 0.1011 0.1010 0.1011 0.1012 0.1010 0.1011 0.1012 0.1014 0.1013 0.1015 0.1016 0.1008 Range 0.0028 0.0048 0.0034 0.0025 0.0026 0.0039 0.0011 0.0007 0.0027 0.0029 0.0031 0.0028 0.0022 0.0013 0.0016 0.0033 0.0022 0.0019 0.0048 0.0022 0.0026 Mean Up Range Up Mean A/B Below Up Up Below Up Down Below Up Down Below Down Up Below Up Up Below Up Down Below Up Down Up Up Above Up Up Above Down Up Above Up Down Above Up Down Above Down Down Above Up Up Above Up Up Above Up Down Above Down Down Above Up Up Above Up Down Above Range A/B Above Above Above Below Below Above Below Below Above Above Above Above Below Below Below Above Below Below Above Below 12 13 14 15 16 0.1020 17 18 19 20 0.1013 0.1021 0.1024 0.1026 Average Runs Observed Runs Expected Sigma SDs You can fill in the area in yellow with formulas if you like...not required