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If a piece of toast falls off your breakfast plate, is it more likely to land with the buttered side down? According to Murphys Law (the assumption that if anything can go wrong, it will), the answer is Yes. Most scientists would argue that by the law of probability, the toast is equally likely to land butter-side up or butter-side down. Robert Matthews, science correspondent of the Sunday Telegraph, disagrees. He claims that when toast falls off a plate that is being carried at a typical height, the toast has just enough time to rotate once (landing butter-side down) before it lands. To test his claim, Mr. Matthews has arranged for 150,000 students in Great Britain to carry out the experiment with tumbling toast.
Assuming scientists are correct, the proportion of times that the toast will land butter-side down is p = 0.5. We can use a coin toss to simulate the experiment. Let heads represent the toast landing butter-side up.
a) Toss a coin 5 times and record the proportion of heads obtained, EMBED Equation.3 (number of heads)/5. Explain how your result relates to the tumbling-toast experiment.
b) Repeat this sampling process 5 times. Make a dotplot of the 5 values of EMBED Equation.3 . Is the center of your distribution close to 0.5?
c) Five repetitions give a very crude approximation to the sampling distribution. Pool your results with the rest of the class to obtain many repetitions. Make a histogram of all the values of EMBED Equation.3 . Is the center close to 0.5? Is the shape approximately normal?
d) How much sampling variability is present? That is, how much do your values of EMBED Equation.3 based on sample sizes of size 5 differ from the actual population proportion, EMBED Equation.3 0.5?
e) Now repeat parts (a) to (d), but this time toss the coin 15 times.
f) Now repeat parts (a) to (d), but this time toss the coin 40 times.
g) Why do you think Mr. Matthews is asking so many students to participate in his experiment?
What happened in the experiment with the students and the toast?
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