Hi, Im struggling to understand this Management 361 issue, titled the "Rat Freeze Case".

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 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. He owed 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 went right to work killing 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. The trap user could simply pitch the frozen rat into the garbage and that was that. Poindexter's advertising proudly proclaimed, "Your rat will move less than an inch or I'll eat it and give you're your money back!" 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...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 surely 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 embarrassed whenever one of his billionaire friends saw him flying around in a jet that was almost a full year old. What to do? 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. The diameters are normally distributed. That dataset can be found on the first sheet in the Excel workbook (labeled "50 Throat Diameters"). Poindexter's specification on that diameter was 0.1000 plus or minus 0.0050. The second dataset (which can be found on the sheet 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 possibly after a problem had developed at the supplier. That is, this sample was taken when the process may or may not have been under control...we just don't know. Each horizontal row in the second dataset represents one sample consisting of 5 observations (5 diameters). Each row gives that sample's 5 individual diameters in columns B to F, then gives the whole sample's mean diameter in column H, and the sample's range of diameters 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 still under control or if it was still 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 manufacturing 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?

Does the first dataset show that the process had a problem two months ago (yes or no)? If yes, which type of problem did it have? Show whatever calculations/charts you need to support your answer. You may or may not need both calculations and charts. No points will be awarded for unsupported answers since they may be just wild guesses.

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