Question

a.       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? please explain decision

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? Why?

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?

Answer 1

1. When take I deal of 4 cards, sometimes I get one card of each suit that is 25% of each suit but it is not always the case.

2. Sometimes I get all four cards of on the same suit by that I me wrongly judge that all the cards of the Deck belonging to only one suit, hence I understand that based on one single sample we cannot make a decision about the deck.

3. By taking the average of sample proportions for 10 samples we get close to 25% of each suit, by this we understand that taking more number of samples we get accurate estimate of the population. Here that is the Deck.

4. When we take three cards sample, I see that I can never get 25% of each suit, hence observe that for making an estimate it’s important to know the number of cards that I taken a sample and I have to choose the number which is the integer multiple of 4

5. Same is the case when I take 5 cards in a sample I can never get 25% of each sample

6. From the above activities, we conclude that to estimate about the deck, it’s important to take the number of cards in the sample as the integer number of 4 and it is important that I make large number of repetitions of the sample that is I had to take a large number of samples before I make a conclusion

7. As we take more number of samples, that is 10 26 , 51 and 52, I see that I am getting more precise estimation of the Deck and its contents hence the summaries we have to take more number of samples to make efficient estimation.