A market research company has approached you about the possibility of using its services to help you decide whether to launch a new product. According to its customer portfolio, it has correctly predicted a favorable market for its clients' products 18 out of the last 20 times. It has also correctly predicted an unfavorable market for its clients' products 9 out of 12 times. Without this research company's help, you have estimated the probability of a favorable market at 0.58. Calculate the posterior probabilities, using the track record of the research firm.

Apparently, depression significantly increases the risk of developing dementia later in lift (BBC News, July 6, 2010). In a recent study it was reported that 22% of those who had depression went on to develop dementia, compared to only 17% of those who did not have depression. Suppose 10% of all people suffer from depression.   What is the probability of a person developing dementia?   If a person has developed dementia, what is the probability that the person suffered from depression earlier in life?

A political scientist claims that 38% of first-year college students characterize themselves as being “moderate” or “middle of the road” as far as their political affiliation is concerned.   Believing this claimed value is too high, you survey a random sample of 400 first-year college students and find that 120 characterize themselves as being “moderate” or “middle of the road.”    Based on this information, what will the test statistic be? Choose the answer below that is closest to what you calculate, and try not to do a lot of rounding until you get to the very end of your calculations.   1. -0.3 2. -1.2 3. -2.6 4. -3.3 5. None of the other answer options are correct because the test statistic should be positive, not negative.

Interpret the effect of temperature on the odds of thermal distress. Test the hypothesis that temperature has no effect, using (i) the Wald test, (ii) the likelihood-ratio test.

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A dowser has correctly located water for a well 1 out of 2 times in Jones County. In Jones County, someone who is just guessing has a 40% chance of locating water for a well. Does this sample provide sufficient evidence that the dowser can locate water and is not just guessing?

If one rejects the null hypothesis at the 5% level, then there is a 5% chance that you made the wrong decision. True /False