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X1-X2-10 24. Consider the test HoHa-μ2-10 vs. μι-μ2 > 10 using the test statistic z-1-2 n1 n2 Suppose throughout that σ1-15 and σ2 20. a) Find the p-value if X1 -145.8 based on 50 samples and X2 -130.1 based on 50 samples b) Assume that the significance level of the test is 0.03. What is the conclusion?If it turns out that the conclusion was an error, is it a type I or type II error? c) Assuming the significance level is 0.03, and the sample sizes are both 100, what is the probability that the test will fail to recognize that Ho is false, when in reality ui - H2 -13. Assuming ni = n,-N, how large should N be so that the probability of part c) is 0.05 or less? d) 25. We will now apply a proportions test to the psychic situation of problem 18. The test is Ho p 0.20 vs. НАгр 0.20. If the null hypothesis is rejected, the conclusion is the subject has ESP (extrasensory perception). Otherwise the person is deemed a random guesser. a) What is a type I error in this situation? b) What is a type II error in this situation? c) If the significance level is 0.04, what proportion of random guessers will be incorrectly identified as having ESP? d) Suppose that people with psychic ability were to exist. Assume for simplicity their powers are such that they have an actual probability of p - 0.21 of guessing correctly. If a significance level 0.04 test is used, what proportion of these people will be identified as random guessers? (n -200 cards) e) What is the p-value of a test subject getting 55 correct out of 200,Does this p-value depend on the 0.04 significance level?

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