Hello. I did a experiment to calculate a magic trick in assignment 1. I have listed the question and answer and the below attachments. I got full marks so I know the results are right. Now in assignment 2, number 6 it asks us to construct a 95% CI and a hypothesis test. I'm having difficulty doing this so if someone could help me with number 6 a and b I would very much appreciate it. Thank you, the 1st attachment is the question that I need help with. The 95% confidence interval, and the 2nd and 3rd attachments are the question and answer from assignment 1 for the card trick.
d3cgwrxphzOfqu.cloudfront.net C D https://d3cgwrxphzOfqu.cloudfront.net/62/f2/62f2fada64c134b4375 ge - my.monash Question 6 [8 Marks] A magician performs the following card trick. She asks a volunteer to secretly select a number between 1 and 13 and deal that number of cards from a well-shuffled face- down pile of 52 standard playing cards to form a face-up pile. The last card dealt determines a new number of additional cards to be dealt from the face-down pile to the face-up pile: if it is an ace, the new number is 1; if it is Jack, Queen or King, the new number is 11, 12 or 13 respectively; otherwise the new number is the face value of the card. This process is continued: at each stage, the last card dealt determines the new number of cards to deal from the face-down pile to the face-up pile. The process ends when the new number to be dealt is larger than the number of cards left in the face-down pile. The volunteer remembers that last number (the number that was too large) and deals any remaining cards from the face-down pile onto the face-up pile. All this is done with the magician out of the room. The magician then enters the room, turns the pile of face-up cards face-down without shuffling and repeats the process, but starting with the number 1 (which may or may not be the initial number chosen by the volunteer). When the trick works, the magician gets the same last number as the volunteer, no matter what number the volunteer started with. But the trick doesn't always work! a) Perform an experiment to estimate the probability the magician and the volunteer end up with the same last number. Give full details of the experiment and result. You may pool results with other students. (Keep your results - you will need them again for Assignment 2!) b) What is the population you are sampling in this experiment? c) Explain why the magician and volunteer are likely to end up with the same last number, no matter what number the volunteer chooses initially. d) If the trick is performed with two decks of 52 cards shuffled together, is it more or less likely to work? Justify your answer. o) [ markzal Each ronout of the avnoriment should involve. MAY tv D 9 A X chosen Lung By cel mor Am number generator or other random generatorAssignment 2-$1-2021.pdf A Q Search age 4 of 4 Question 6 [8 Marks] Recall the card trick from Question 6 of Assignment 1. Use your results from the experiment that you performed for that question, or generate new results, to perform the following tasks. a) Construct a 95% confidence interval for the probability the magician and volunteer both end up with the same card. b) A theoretical analysis predicts that this probability should be approximately 85%. Perform a hypothesis test at the 0.05 significance level to determine whether your results are consistent with this prediction. (End of assignment) tv D MAY 9 4 W6) a. To do this experiment, I used an online card shuffler. I randomly picked a number from 1 to 13 and using the online card shuffler, I would draw out the number of cards of the chosen number from 1-13 and I would record the sequences of the cards I drew and also the card numbers. For example, from numbers 1-13, I chose 7, then the number of cards I should draw face up is 7 from the deck and whatever the value on the card is, I record it and also I record the previous 6 cards that was drawn before the 7th . Once this is done, I shuffle the deck and I then repeat this process 16 times and for every time I draw a card I would reshuffle the deck. Out of these 16 times, I record all the number of times the volunteer and magician end up with the same number, which is 12. So, the probability of this trick working is 12/16 - 0.75. b. The population that we are sampling are the trials of outcome, which is the pair, representing the final card drawn by a volunteer and by the magician. c. When the magician and volunteer end up with the same last number, the entire sequence of numbers is the same. The magician will use the same pattern again to end up with the same last number again. This is a sort of coupling technique. d. It's more likely to work even if the deck size increases. This is because the probability of the trick working is going to increase and the probability of the trick not working is going to decrease. Focus D MAY 9 A W P X
