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It has been claimed that, for a penny minted in 1999 or
Chapter 9, Problem 6E(choose chapter or problem)
Problem 6E
It has been claimed that, for a penny minted in 1999 or earlier, the probability of observing heads upon spinning the penny is p = 0.30. Three students got together, and they would each spin a penny and record the number X of heads out of the three spins. They repeated this experiment n = 200 times, observing 0, 1, 2, and 3 heads 57, 95, 38, and 10 times, respectively. Use these data to test the hypotheses that X is b(3, 0.30). Give limits for the p-value of this test. In addition, out of the 600 spins, calculate the number of heads occurring and then a 95% confidence interval for p.
Questions & Answers
QUESTION:
Problem 6E
It has been claimed that, for a penny minted in 1999 or earlier, the probability of observing heads upon spinning the penny is p = 0.30. Three students got together, and they would each spin a penny and record the number X of heads out of the three spins. They repeated this experiment n = 200 times, observing 0, 1, 2, and 3 heads 57, 95, 38, and 10 times, respectively. Use these data to test the hypotheses that X is b(3, 0.30). Give limits for the p-value of this test. In addition, out of the 600 spins, calculate the number of heads occurring and then a 95% confidence interval for p.
ANSWER:
Step 1 of 8
According to the null hypothesis,
Then, calculate the probabilities of getting 0, 1, 2, and 3 heads, assuming that the null hypothesis is true, as follows,
