# Gregg Miller - Central Piedmont Community College - Charlotte, NC

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Gregg Miller - Central Piedmont Community College - Charlotte, NC gregg.miller@cpcc.edu

 Purpose: To introduce students to the thought process involved in hypothesis testing  Source: Journal of Statistics Education v.2, n.1 (1994) Steven Eckert, Texas A&M (http://www.amstat.org/publications/jse/v2n1 /eckert.html )http://www.amstat.org/publications/jse/v2n1 /eckert.html

 Two decks of cards with identical backs  Re-mix the decks so that one deck of 52 is all red.

 Remind students of the content of a standard deck of cards  What is the probability of randomly selecting a red card from a standard deck? A black card?  If we randomly select 10 cards from the deck, one at a time, with replacement, how many red cards do we expect? How many black?  Begin selecting cards, one at a time with replacement

 Continue drawing cards, noting the color, until a student comments about being suspicious  Poll the class to see how many are convinced the deck is fixed, how many suspect so, and how many aren’t sure  Continue drawing cards until all are convinced  Poll the class again to determine the number of red cards it took for the students to conclude the deck was fixed

 Draw parallels between the red deck experiment and the stages in hypothesis testing Card DeckHypothesis Testing Initially assumed a standard deckNull hypothesis Drew cards and noted the colorData collection Noticed that the results weren’t turning out approx. half red, half black Compare observed to expected Decided the deck wasn’t standard (“This is too weird”) Reject null hypothesis Concluded deck was fixedAccept alternative hypothesis

# of red cards in a rowProbability, assuming standard deck (p-value) 1.5 2.25 3.125 4.0625 5.03125 6.015625 7.0078125 Compare p-values for the number of cards to traditional values of α=.10 (between 3 and 4 cards), α=.05 (between 4 and 5 cards), and α=.01 (between 6 and 7 cards)

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