According to statistician Persi Diaconis, the probability of a penny landing heads when it is spun on its edge is only about 0.20. Suppose you doubt this claim and think that it should be more than 0.20. To test this, you spin a penny 12 times and it lands heads side up 5 times. You put this information in the One Proportion applet and determine a simulation-based p-value of 0.0770, but the one-proportion z-test p-value is 0.0303.
a. Write down the hypotheses for this study.
b. Which p-value would you say is the most valid? Explain.

c. Do you have strong evidence that a spun penny will land heads more that 20% of the time in the long run?

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300 |0.0770 Probability of success (T): 0.2 12 Sample size (n): 200 1000 Number of samples: Animate 100 Draw Samples Total = 1000 6. O Number of successes O Proportion of successes 25 Number of successes Count As extreme as O Summary stats Proportion of samples: 77/1000 = 0.0770 All attempts (last sample) I Two-sided O Exact Binomial Normal Approximation p-value = 0.0303 (Z = 1.88) Successes (last sample) = 2