TMGT 361

  
Initial Post
See the general assignment instructions for information about the quality and quantity expectations and evaluation criteria. 
VI. Sampling and measurement. Write up the results of the following, answering the questions, discussing any results and interpretations.*
a. Get a deck of standard playing cards. Let the deck be the lot or population (n=52; don’t use the jokers). Shuffle the deck 7 times. Assume the king of hearts (the suicide king) is a defect. A good deck has no defects; a bad deck has at least one defect. What is the proportion defective based on what you know about the deck?
Pretend you don’t know anything about the population (the deck, because in real life you don’t; you only can make estimates of the population based on samples). Based only on the sample do the following (remember, you don’t know what is in the deck, you don’t know if there is a suicide king or not). Draw a random sample of 4 cards. Did you get a defect? Do you have a good or bad deck? 
Return the sample of 4 to the deck (sampling with replacement) and draw another sample of 4 and repeat: for this sample, do you have a good deck or not?
b. Assume a good deck is 25% of each suit (out of 52 cards, there are 13 each of hearts, spades, diamonds, and clubs). Deal 4 cards. Did you get 25% of each suit? (You can just focus on one suit if you want; you will learn the same thing.) Why or why not? Basing your decision only on the sample, do you have good deck or not? 
Put the 4 cards back and reshuffle. Repeat the above. Do this for a total of 10 samples. Average the 10 sample proportions for all 4 suits. What can you conclude about a single sample compared to the population? What can you conclude about the average of sample proportions compared to a single sample? What can you conclude about the average of sample proportions compared to the population?
Draw a sample of 3 cards. From this sample only is it possible to get 25% of each suit? Replace the sample of 3 and draw a sample of 1. Repeat with a sample of 5. Is it possible to get 25% of each suit? What conclusions can you draw from this?
With replacement, draw a sample of 10, 26, 51, and 52 (the entire population). What was the proportion of the suits for each sample? What can you conclude about the results? 
c. Shuffle the deck and put it face down. Randomly remove one card and keep it face down so that you do not know what card was removed and which ones remain. Deal a sample of 4 cards. Do you have a good deck (25% of each suit)? With replacement, deal samples of 25 and 51. What can you conclude about the results?
Do all the preceding yourself (you can use someone else’s cards :). The point is for you to experience first-hand how random error can and will make the sample results, e.g., the cards you dealt, be different from the population. With any wisdom and life experience at all, you already know this. But you might not have thought about it the way we need to in this class. Note that you are being prepared to understand the concept and perform a test (judge or conclude) to see if the results you expect (from knowing about the population) are similar or not to what you got in the sample.