Obj: SWBAT conduct experiment simulations using Table B and the calculator'

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Obj SWBAT conduct experiment simulations using
Table B and the calculator.

• Drill
• Shampoo is on sale. The sign reads, Buy one, buy
  the second at half price. What is the total
  discount on the purchase of two bottles of
  shampoo?
• The original marked price of a DVD player was
  300. The DVD player has been on sale with
  successive discounts of 25 and 10. What is the
  present price of the DVD player?

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S5.3 Day 1

• Simulating Experiments

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Three methods to answer questions involving
chance

• Actually carry out the experiment many times
  calculate the results relative frequency.
• Develop a probability model.
• Start with a model that reflects the truth about
  the experiment, and then develop a method of
  simulating a number of repetitions for the
  experiment.

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Steps in a Simulation

• State the problem or describe the experiment.
• State the assumptions.
• Assign digits to represent outcomes.
• Simulate many repetitions.
• State your conclusions.

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Steps in a Simulation

• State the problem or describe the experiment.
• Toss a coin 10 times. What is the likelihood of a
  run of at least 3 consecutive heads or 3
  consecutive tails?
• State the assumptions.
• Head Tail are equally likely to occur on each
  toss
• Tosses are independent of each other

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Steps in a Simulation

• Assign digits to represent outcomes.
• Table B assigns the digits 0, 1, 2, 3, 4, 5, 6,
  7, 8, 9 randomly
• The successive digits in the table are
  independent
• One digit simulates one toss of the coin
• Odd digits represent head even digits represent
  tails

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Steps in a Simulation

• Simulate many repetitions.
• Looking at 10 consecutive digits in Table B
  simulate one repetition
• Of 25 total repetitions, 23 of them had a run of
  head or tails.
• State your conclusions.
• We estimate the probability by 23/25 0.92
• You can tell a computer to do many thousands of
  repetitions.
• A long simulation finds that the true probability
  is about 0.826

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Exercise 5.59

• A coin
• A six-sided die
• A random digit table
• A standard deck of playing cards

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Exercise 5.60

• How could you use the two coins to set up your
  simulation?

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Exercise 5.61

• How would you pose this question to 10 students
  independently of each other? How would you model
  the procedure?
• Assign digits to represent the answers yes and
  no.
• Simulate 5 repetitions, using Table B.
• Combine your results with the rest of the class.
• What is the estimate of the likelihood of the
  desired result?

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HOMEWORK

• Do 62-63
• Do 74 80 (Chapter Review)

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Chapter 5

• Review

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Obj SW review Chapter 5

• Drill

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McDonalds vs. Wendys (5.82)

• Do consumers prefer the taste of a cheeseburger
  from McDonalds or from Wendys in a blind test
  in which neither burger is identified? Describe
  the design of a matched pairs experiment to
  investigate this question.

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Repairing Knees in Comfort (5.83)

• Knee injuries are routinely repaired by
  arthroscopic surgery that does not require
  opening up the knee. Can we reduce patient
  discomfort by giving them a nonsteroidal
  anti-inflammatory drug (NSAID)? 83 patients were
  placed in three groups.
• Group A received NSAID before after surgery
• Group B received placebo before NSAID after
• Group C received placebo before after surgery
• The patients recorded a pain score by answering
  questions one day after the surgery

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Repairing Knees in Comfort (5.83)

• Outline the design of this experiment. You do not
  need to do the randomization that your desing
  requires.
• You read that the patients, physicians
  physical therapists were blinded during the
  study. What does this mean?
• You also read that the pain scores for Group A
  were significantly lower than Group C but not
  significantly lower than Group B. What does this
  mean? What does this finding lead you to conclude
  about the use of NSAIDs?

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Hot Streaks in Foul Shooting

• Joey is interested in investigating so-called hot
  streaks in foul shooting among basketball
  players. Hes a fan of Danielle, who has been
  making approximately 80 of her free throws.
  Specifically, Joey want to use simulation methods
  to determine Carlas longest run of baskets on
  average, for 20 consecutive free throws.

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Hot Streaks in Foul Shooting

• Describe a correspondence between random numbers
  and outcomes.
• What ill constitute one repetition in this
  simulation?
• Carry out 20 repetitions record the longest run
  for each repetition.
• Combine your results with those of 4 other
  students to obtain at least 100 replications.
• What is the mean run length? Are you surprised?
• Determine the 5-number summary for the data.
• Construct a histogram of the results.