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A psychologist is studying smokers' self-images, which she measures using the self-image (SI) score from a personality inventory. She would like to examine the mean SI score 1.1 for the @pulation of all smokers. Previously published studies have indicated that the mean SI soore for the population of all smokers is 85 and that the standard deviation is 15, but the psychologist believes that the value for the mean has decreased. She decides to perform a statistical test and chooses a random sampl_e of 50 smokers' SI scores. She'll use the value 15 lor the population standard deviation, and she'll test at the 0.1 level of significance. Based on this information. answer the questions below. Carryr your intermediate oomputations to at least four decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.) V What are the null and altematlve hypotheses that the psychologist should use for the test? What is the probability that the psychologist commits a Type I error? Round your response to at least two decimal places. pis ? v ? v ills I? v ? vl Assuming that the actual value of u is 32, what is the probability that the psychologist rejects the null hypothesis? Round your response to at least two decimal places. Suppose that the psychologist decides to perform another statistical test using the same population, the same null and alternative hypotheses, and the same sample size, but for this second test the psychologist uses a signicance level of 0.05 instead of a signicance level of 0.1. Assuming that the actual value of |.| is 82, how does the probability that the psychologist commits a Type II error in this second test compare to the probability that the psychologist commits a Wpe II error in the original test? O O O The probability of committing a Type II error in the second test Is greater The probability of committing a Type II error in the second test Is less The probabilities of committing a Type II error are equal