Poindexter LeMans sat at his Louis XIV desk and looked at the garage monitor. Sure enough, there was his Lamborghini Veneno parked snuggly in the middle of his other 50 cars. He thought to himself, "Sure $4,500,000 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?" As you might have guessed Poindexter had a very successful career going or else he wouldn't have had such expensive trappings, and probably would have been fired for goofing off. And you'd 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 it all 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 went right to work; he killed 52 rats in the first 24 hours (still a record for a 6-year-old orphan). By the time he was 18 environmentalists feared that rats would become extinct. Fortunately (for the rats) Poindexter 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 use for 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 beloved hammer), he had discovered a clean and fast 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, a really huge rat could eat it and still have just enough life force remaining 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 Poindexter's Rat-Freeze trap, even a giant cat-sized rat couldn't 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). The trap user could simply pitch the frozen rat into the garbage and that was that. Poindexter's advertising proudly proclaimed, "The rat will move less than an inch or I'll 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 customer's money and ate the rat, as promised, but his private chef had prepared the

creature in a nice barnaise sauce, so it wasn't too bad...the smaller bones were a little crunchy, but not bad otherwise...no more disgusting than Buffalo Wings. Poindexter's 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 that his trap wasn't as good as advertised. Sales would suffer; his customers, like himself, demanded exactly what was promised. Furthermore, although the rat he ate had been tolerable, he didn't really want to eat more than one rat a year. 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 trap's 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. The Datasets Poindexter has two datasets to use in exploring the problem. The first dataset was obtained two months ago when the process was known to be definitely under control. It consists of 50 individual nozzle diameters and is normally distributed. That dataset can be found on the first sheet in the Excel file (the sheet labeled "50 Throat Diameters"). Poindexter's specification on that diameter was 0.1000 plus or minus 0.0050. 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 (just a week ago) and probably after a problem had developed at the supplier (if there really is a problem in the supplier's operation). Each horizontal row in that second dataset represents one sample consisting of five observations. Each row gives that sample's five observations in columns B to F, then gives that sample's mean in column H, and finally that sample's 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 don't know if the process was under control or if it was 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 supplier's process or there really isn't really a problem at all (the fact that the rat didn't die instantly was just a very unlikely fluke perhaps the rat in question had especially good genetics, ate well, and exercised often). You need to find out what the truth is; is there a problem with the supplier's process or not?

The Assignment (540 Points Total) The case point will be graded as follows: 40 points for the correct form (the "Form Requirements" are shown next). 500 points for correct answers to the questions. REPORT FORM REQUIREMENTS: These are "free" points that I am giving you. They don't require any thinking. You get 10 points for each of the following four report form requirements. Everyone should get all 40 points by just doing the following: 1. Submit your assignment in one word or pdf file uploaded from the Rat Freeze assignment (under assignments in Canvas). You may draw your charts and do your calculations by hand or let excel draw the charts and do the calculations for you. You answers by hand or type them in a word document. However, regardless of how many different types of software you use, you need to submit your assignment in one file. This can be done, of course, by scanning all your handwritten work into one pdf file, etc. Your answers must be in order so scan your answers in order...do not put charts etc. in an appendix separate from the question you are answering...everything you submit to answer a question must in one place. 10 Points 2. Do not put your name on your assignment. Canvas will let me know who submitted it. After I'm finished grading your case it will be used for "assurance of learning" which requires my colleagues to evaluate it without knowing who submitted it. 10 Points 3. Number your answers so I will know which answer goes with which question, and when one answer ends and the next one begins. 10 Points 4. Your file must readable. Do not submit illegible writing or poorly scanned pages...if I can't read your writing or see your work I'll have to count it as wrong. To avoid a problem, you should look at any scanned files before you upload them. 10 Points QUESTIONS: Answer the following questions. Again, make sure that you number them. Do not repeat the questions in your answer. I know the questions and your answers will be numbered. Question 2 (100 points): Does the first dataset prove that either of those problems existed two months ago? If so, which type of problem may have happened then? Answer in or fewer. Also show whatever calculations or charts you used to

answer the question. Note: You will not get any points for unsupported answers so you will need to have some calculations or charts to prove that your answer is correct. Question 3 (100 points): Does the second dataset prove that either of those problems existed a week ago? If so, which type? Answer in or fewer and, once again, show whatever calculations or charts you need to prove that your answer is correct. Again, unsupported answers will not receive any points. Question 4 (100 points): Your answer to one of the last two questions will require drawing a chart or two. Which question required you to draw a chart(s)? Why was a chart necessary? Answer in Question 5 (100 points): Say which of the following is true at present (starting a week ago) and then say why it is true. Only one of the four is true right now so only pick one. You lose all 100 points if your pick two or more...so (again) only pick one. Answer using A. The process is presently under control, and is good enough. B. The process is presently under control, but not good enough. C. The process is not under control now, but was good enough when it was under control two months ago. D. The process is not under control now, and it wasn't good enough when it was under control two months ago. You have all the data you need to answer the questions. Any number you need can either be calculated from the ones you have been given (like a standard deviation can) or is a matter of your managerial discretion (in which case you need to pick a number that makes sense). For example, if you need to come up with a cutoff number for a particular test and it isn't given, then you need to decide what it should be. In that case (of managerial discretion) make sure to tell me what number you picked and why. Specifically, maybe 3 standard deviations makes sense for a cutoff; or maybe an industry standard number makes sense. You decide. Hint: If there is an industry standard number you'll probably find it in the text, right? If you need a number that can be calculated (like a standard deviation, average, average of averages, average of ranges, etc.) you may calculate it by hand or have excel calculate it for you. Be careful when calculating standard deviations, average etc. ... there are sometimes two formulas you can use for the same thing and each formula uses a different standard deviation. Remember that the standard deviation of a process is larger than the standard deviation of sample averages from that process, so it makes a difference which standard deviation you use in a given formula. As a check on your work, you could use two our 3 formulas to calculate the same thing and see if you get the same results. In those cases where you can use more than one formula, you can use them all (as I just noted...to check your work) or you can pick whichever formula you prefer. Again, if you are doing things right all the formulas should give you the same result.

Item # Throat Diameters 1 0.1011 2 0.1011 3 0.0999 4 0.1009 5 0.1008 6 0.0997 7 0.1028 8 0.0991 9 0.0989 10 0.1001 11 0.0996 12 0.0996 13 0.1026 14 0.1016 15 0.1020 16 0.1027 17 0.1012 18 0.1005 19 0.1006 20 0.1010 21 0.1037 22 0.1011 23 0.1013 24 0.0989 25 0.1024 26 0.1026 27 0.1004 28 0.1007 29 0.1021 30 0.1013 31 0.0998 32 0.0991 33 0.1016 34 0.1012 35 0.0992 36 0.1004 37 0.1021 38 0.1023 39 0.1002 40 0.1021 41 0.0982 42 0.1007 43 0.1002 44 0.1011 45 0.1008 46 0.1014 47 0.0997 48 0.1020 49 0.1025 50 0.0997

Sample Mean Range Mean Up Range Up Mean A/B Range A/B 1 0.0982 0.0989 0.1010 0.0993 0.1005 0.0996 0.0028 Below Above 2 0.0997 0.1028 0.0991 0.0980 0.1001 0.0999 0.0048 Up Up Below Above 3 0.0998 0.1001 0.1025 0.0991 0.0991 0.1001 0.0034 Up Down Below Above 4 0.0998 0.0991 0.1016 0.1012 0.0992 0.1002 0.0025 Up Down Below Below 5 0.0982 0.1007 0.1002 0.1000 0.1008 0.1000 0.0026 Down Up Below Below 6 0.1028 0.0989 0.1008 0.0997 0.1016 0.1007 0.0039 Up Up Below Above 7 0.1011 0.1011 0.0999 0.1009 0.1008 0.1008 0.0011 Up Down Below Below 8 0.1011 0.1006 0.1013 0.1011 0.1007 0.1009 0.0007 Up Down Above Below 9 0.1026 0.1008 0.1011 0.1004 0.0999 0.1010 0.0027 Up Up Above Above 10 0.1014 0.0997 0.1020 0.1025 0.0997 0.1011 0.0029 Up Up Above Above 11 0.0996 0.0996 0.1026 0.1010 0.1020 0.1010 0.0031 Down Up Above Above 12 0.0996 0.1021 0.1021 0.0996 0.1023 0.1011 0.0028 Up Down Above Above 13 0.1027 0.1012 0.1005 0.1006 0.1010 0.1012 0.0022 Up Down Above Below 14 0.1012 0.1012 0.1008 0.1015 0.1002 0.1010 0.0013 Down Down Above Below 15 0.1014 0.1016 0.1015 0.1000 0.1010 0.1011 0.0016 Up Up Above Below 16 0.1011 0.1002 0.0997 0.1030 0.1020 0.1012 0.0033 Up Up Above Above 17 0.1026 0.1004 0.1007 0.1021 0.1013 0.1014 0.0022 Up Down Above Below 18 0.1004 0.1021 0.1017 0.1002 0.1021 0.1013 0.0019 Down Down Above Below 19 0.1037 0.1011 0.1013 0.0989 0.1024 0.1015 0.0048 Up Up Above Above 20 0.1004 0.1009 0.1020 0.1021 0.1026 0.1016 0.0022 Up Down Above Below Average 0.1008 0.0026 Runs Observed R