Assuming the null hypotheses are true, each of the three tests in Question 29 has a 5% chance of inappropriately rejecting the null hypothesis. However, the probability that at least one of the three tests will inappropriately reject the null hypothesis is 14.26%. Assuming that the null hypothesis is true and that each test is independent, complete the following steps to convince yourself that this probability (14.26%) is correct.
a. Each test will either reject (R) or fail to reject (F). List the rest of the eight possible outcomes in the table below.

b. The probability that each hypothesis test rejects is P(R) = 0.05, and the probability that each hypothesis test fails to reject is P(F) = 0.95. You may recall that when events are independent, the probabilities can be multiplied.
For example, the probability that all three tests fail to reject is P(F) P(F) P(F) = 0.95 * 0.95 * 0.95 = 0.8574. Similarly, the probability that the first two tests fail to reject and the third test does reject is 0.95 * 0.95 * 0.05 = 0.0451.
Complete the table by calculating the probabilities for all eight cases. Verify that the eight probabilities sum to one.
Case 1 is the only case where no test is rejected. The probability that at least one test rejects is the sum of the probabilities for cases 2 through 8; more simply, the probability that at least one test rejects can be calculated as 1 €“ 0.8574 = 0.1426.

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Case TeTs 2 Test ability 4