1.10. (-) On July 4, 1995, the New York Times reported that the nation's uni- versities were awarding 25% more Ph.D. degrees than the economy could absorb. The headline concluded that there was a 1 in 4 chance of underemployment. Here "underemployment” means having no job or having a job not requiring the Ph.D. degree. What should the correct statement of the odds have been?
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Here, according to the reports, number of person not getting a job or getting a job not requiring phd is 1 out of 4 persons.
i.e., the system could give job to 3/4th portion of Ph.D.s
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- I personally have used statistics in trying to challenge the reliability of drug testing results. Suppose the chance of a mistake in the taking and processing of a urine sample for a drug test is just 1 in 100. And your client has a "dirty" (i.e., positive) test result. Only a 1 in 100 chance that it could be wrong? Not necessarily. If the vast majority of all tests given-say 99 in 100-are truly clean, then you get one false dirty and one true dirty in every 100 tests, so that half of the dirty tests are false. Define the following events as: TD = TC = D = event that the person tested is actually dirty C = event that the person tested is actually clean (a) Using the information in the quote, find the values of each of the following. event that the test result is dirty event that the test result is clean (i) P(TD|D) (ii) P(TDIC) (iii) P(C) (iv) P(D) X X (b) Use the law of total probability to find P(TD). (c) Use Bayes' rule to evaluate P(C|TD). XA hospital administrator finds that the mean hospital stay for a sample of 77 women after childbirth is 3.1 days. She claims that the mean stay at her hospital is greater than the national average of 2.7 days. Assuming that the average at her hospital is the same as the national average, the probability of observing a sample with a mean of 3.1 days or more is 0.16. Formulate the null and alternative hypotheses. Then discuss whether the sample provides evidence for rejecting or not rejecting the null hypothesis. Assume a significance level of 0.05.What would be the percentage of this question?
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