Stacked Deck?

How much evidence do you need to be confident in your answer?

A DataClassroom simulation activity


Background

A standard deck of cards contains 52 cards, 26 that are red and 26 that are black. Thus you can assume that with a fair deck, the chance of blindly pulling a red card from a well shuffled deck 50%. Your teacher has built a simulated card deck in DataClassroom. Your teacher may have created the simulated deck with an equal probability of selecting either a red or black card, or they may have created an unfair deck where either red or black cards have been removed and replaced by cards of the opposite color from another deck.  

Use the simulation that has been built for you to select cards from the simulated deck. You will be sampling cards with replacement. That means that you can picture drawing a card, recording it as either red or black,  returning it to the deck, and reshuffling so the probability of drawing either a red or a black card is not affected by the previous cards that you selected.

Variable

Card Color- This categorical variable has only two fixed values; either it is red or it is black.

Activity

  1.  Give your teacher the benefit of the doubt and assume that they have given you a simulated deck of cards that is fair. What is the probability (expressed as a decimal) of pulling a red card from the deck? 


  2. In this activity, you suspect that your teacher may have built a simulated card deck that is not a fair deck. What is the null hypothesis that you will be testing and what is the alternative? 

    Write your hypothesis in terms of one color.

  3. Let’s begin collecting data to test your null hypothesis from #2. Draw a single card from the simulated deck by pressing the red Go button. How confident are you that the deck is either fair or unfair based on your first card draw? 


    *Note that your teacher has turned off the New Run on the simulator, meaning each time you select a card, the card color data will be added to the same dataset that you will collect throughout the activity.

  4. Begin to fill in the table below. Continue to fill in the table every time you draw another card in this activity. Record your confidence as a percentage. 100% means you are certain that the deck is fair and 0% means you are certain that it is unfair.

    See table on answer key or on the student facing assignment.

  5. Draw three more cards, one at a time, so that your dataset has four  cards total.  Fill in the first four rows of the table above.

  6. How confident are you now (after drawing 4 cards total) that the deck is either fair or unfair based on the four cards that you have drawn?

  7. Continue to draw one card at a time and complete the table above up to the point where you have drawn nine cards.

  8. After drawing nine cards, describe how your confidence in whether or not the deck was fair changed?

  9. Compare your results to those of your classmates. Do the conclusions drawn around the class vary? What can explain that variation?

  10.  Now set the generate #samples (upper left on the simulator) to add 991 samples to your dataset. Press Go.

  11.  What is the total number of balck cards drawn in your new dataset of 1000 simulated  draws? 

  12.  If this simulated deck of cards  represents a real deck with 52 cards, how many do you think are black and how many are red? 

  13.  How confident are you that you are close to knowing the true number of red and black cards in the deck? 


  14.  How does your response to #12 compare to the class results? Do the class results change your confidence in your response? Why or why not?


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