1) Write the null and alternative hypotheses you would use to test each of the following situations

a) A governor is concerned about his "negatives"-the percentage of state residents who express disapproval of his job performance. His political committee pays for a series of TV ads, hoping that they could keep the negatives below 30%. They will use follow up polling to assess the ads' effectiveness.

b) Is a coin fair?

c) Only about 20% of people who try to quit smoking succeed. Sellers of motivational tape claim that listening to the recorded messages can help people quit.

2) The seller of a loaded die claims that it will favor the outcome 6. We don't believe that claim, and roll the die 200 times to test an appropriate hypothesis. Our P-value turns out to be 0.03. Which conclusion is appropriate? Explain. a) There's a 3% chance that the die is fair. b) There's a 97% chance that the die is fair. c) There 's a 3% chance that a loaded die could randomly produce the results we observed, so it's reasonable to conclude that the die is fair. d) There's a 3% chance that a fair die could randomly produce the results we observed, so it's reasonable to conclude that the die is loaded.

3)In the 1980s, it was generally believed that congenital abnormalities affected about 5% of the nation's children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 384 children and found that 46 of them showed signs of an abnormality. Is this strong evidence that the risk has increased? a) Write appropriate hypotheses. c) Perform the mechanic s of the test. What is the P-value? d) Explain carefully what the P-value mean s in context. e) What 's your conclusion? f) Do environmental chemicals cause congenital abnormalities?

4)The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996, 31% of students reported that their mothers had graduated from college. In 2000, responses from 8368 students found that this figure had grown to 32%. Is this evidence of a change in education level among mothers? a) Write appropriate hypotheses. c) Perform the test and find the P-value. d) State your conclusion. e) Do you think this difference is meaningful? Explain.