1.2.23 According to Stanford mathematics and statistics professor Persi Diaconis, the probability a flipped coin that starts out heads up will also land heads up is 0.51. Suppose you want to test this. More specifically, you want to test to determine if the probability that a coin that starts out heads up will also land heads up is more than 0.50. Suppose you flip a coin (that starts out heads up) 100 times and find that it lands heads up 53 of those times. a. If a stands for the probability a coin that starts heads up will also land heads up, write out the hypotheses for this study in symbols. b. Use an applet to conduct a simulation with at least 1,000 repetitions. What is your p-value? Based on your p-value, is there strong evidence that the probability that a coin that starts heads up will also land heads up is more than 0.50? c. Even though the coin in the study landed heads up more than 50% of the time, you should not have found strong evidence that it will land heads up more than 50% of the time in the long run. Does this mean that Diaconis is wrong about his assertion that it will land heads up 51% of the time in the long run? Explain. d. A newspaper article described the 0.51 probability by saying, "This means that if a coin is flipped with its heads side facing up, it will land the same way 51 out of 100 times." What is wrong with this statement?
1.2.23 According to Stanford mathematics and statistics professor Persi Diaconis, the probability a flipped coin that starts out heads up will also land heads up is 0.51. Suppose you want to test this. More specifically, you want to test to determine if the probability that a coin that starts out heads up will also land heads up is more than 0.50. Suppose you flip a coin (that starts out heads up) 100 times and find that it lands heads up 53 of those times. a. If a stands for the probability a coin that starts heads up will also land heads up, write out the hypotheses for this study in symbols. b. Use an applet to conduct a simulation with at least 1,000 repetitions. What is your p-value? Based on your p-value, is there strong evidence that the probability that a coin that starts heads up will also land heads up is more than 0.50? c. Even though the coin in the study landed heads up more than 50% of the time, you should not have found strong evidence that it will land heads up more than 50% of the time in the long run. Does this mean that Diaconis is wrong about his assertion that it will land heads up 51% of the time in the long run? Explain. d. A newspaper article described the 0.51 probability by saying, "This means that if a coin is flipped with its heads side facing up, it will land the same way 51 out of 100 times." What is wrong with this statement?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:1.2.23 According to Stanford mathematics and statistics
professor Persi Diaconis, the probability a flipped coin that
starts out heads up will also land heads up is 0.51. Suppose
you want to test this. More specifically, you want to test to
determine if the probability that a coin that starts out heads
up will also land heads up is more than 0.50. Suppose you
flip a coin (that starts out heads up) 100 times and find that
it lands heads up 53 of those times.
a. If a stands for the probability a coin that starts heads up
will also land heads up, write out the hypotheses for this
study in symbols.
b. Use an applet to conduct a simulation with at least 1,000
repetitions. What is your p-value? Based on your p-value,
is there strong evidence that the probability that a coin that
starts heads up will also land heads up is more than 0.50?
c. Even though the coin in the study landed heads up more
than 50% of the time, you should not have found strong
evidence that it will land heads up more than 50% of
the time in the long run. Does this mean that Diaconis is
wrong about his assertion that it will land heads up 51%
of the time in the long run? Explain.
d. A newspaper article described the 0.51 probability by
saying, "This means that if a coin is flipped with its heads
side facing up, it will land the same way 51 out of 100
times." What is wrong with this statement?
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