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 π 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?