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The website pundittracker.com keeps track of predictions made by individuals in finance, politics, sports, and entertainment. Jim Cramer is a famous TV financial personality and author. Pundittracker monitored 678 of his stock predictions (such as a recommendation to buy the stock) and found that 320 were correct predictions. Treat these 678 predictions as a random sample of all of Cramer's predictions. (a) Determine the sample proportion of predictions Cramer got correct. (b) Suppose that we want to know whether the evidence suggests Cramer is correct less than half the time. State the null and alternative hypotheses. (c) Verify the normal model may be used to determine the \(P\) -value for this hypothesis test. (d) Draw a normal model with area representing the \(P\) -value shaded for this hypothesis test. (e) Determine the \(P\) -value based on the model from part (d). (f) Interpret the \(P\) -value. (g) Based on the \(P\) -value, what does the sample evidence suggest? That is, what is the conclusion of the hypothesis test? Assume an \(\alpha=0.05\) level of significance.

Effects of Alcohol on the Brain In a study published in the American Journal of Psychiatry (157:737-744, May 2000), researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 12 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cubic centimeters \(\left(\mathrm{cm}^{3}\right)\). An analysis of the sample data revealed that the hippocampal volume is approximately normal with \(\bar{x}=8.10 \mathrm{~cm}^{3}\) and \(s=0.7 \mathrm{~cm}^{3}\). Conduct the appropriate test at the \(\alpha=0.01\) level of significance.

According to the National Sleep Foundation, children between the ages of 6 and 11 years should get 10 hours of sleep each night. In a survey of 56 parents of 6 to 11 year olds, it was found that the mean number of hours the children slept was 8.9 with a standard deviation of 3.2. Does the sample data suggest that 6 to 11 year olds are sleeping less than the required amount of time each night? Use the 0.01 level of significance.

In his book, "The Signal and the Noise," Nate Silver analyzed 733 predictions made by experts regarding political events. Of the 733 predictions, 338 were mostly true. (a) Determine the sample proportion of political predictions that were mostly true. (b) Suppose that we want to know whether the evidence suggests the political predictions were mostly true less thar half the time. State the null and alternative hypotheses. (c) Verify the normal model may be used to determine the \(P\) -value for this hypothesis test. (d) Draw a normal model with the area representing the \(P\) -val shaded for this hypothesis test. (e) Determine the \(P\) -value based on the model from part (d). (f) Interpret the \(P\) -value. (g) Based on the \(P\) -value, what does the sample evidence suggest? That is, what is the conclusion of the hypothesis test? Assume an \(\alpha=0.1\) level of significance.

The drug Lipitor is meant to reduce cholesterol and LDL cholesterol. In clinical trials, 19 out of 863 patients taking \(10 \mathrm{mg}\) of Lipitor daily complained of flulike symptoms. Suppose that it is known that \(1.9 \%\) of patients taking competing drugs complain of flulike symptoms. Is there evidence to conclude that more than \(1.9 \%\) of Lipitor users experience flulike symptoms as a side effect at the \(\alpha=0.01\) level of significance?

NCAA rules require the circumference of a softball to be \(12 \pm 0.125\) inches. Suppose that the NCAA also requires that the standard deviation of the softball circumferences not exceed 0.05 inch. A representative from the NCAA believes the manufacturer does not meet this requirement. She collects a random sample of 20 softballs from the production line and finds that \(s=0.09\) inch. Is there enough evidence to support the representative's belief at the \(\alpha=0.05\) level of significance?

According to the National Highway and Traffic Safety Administration, the proportion of fatal traffic accidents in the United States in which the driver had a positive blood alcohol concentration (BAC) is 0.36. Suppose a random sample of 105 traffic fatalities in the state of Hawaii results in 51 that involved a positive BAC. Does the sample evidence suggest that Hawaii has a higher proportion of traffic fatalities involving a positive BAC than the United States at the \(\alpha=0.05\) level of significance?

Age of Death-Row Inmates In \(2002,\) the mean age of an inmate on death row was 40.7 years, according to data from the U.S. Department of Justice. A sociologist wondered whether the mean age of a death-row inmate has changed since then. She randomly selects 32 death-row inmates and finds that their mean age is 38.9 with a standard deviation of 9.6. Construct a \(95 \%\) confidence interval about the mean age. What does the interval imply?

In Problems \(15-22,(a)\) determine the null and alternative hypotheses, (b) explain what it would mean to make a Type I error, and (c) explain what it would mean to make a Type II error. According to the Centers for Disease Control and Prevention, \(19.6 \%\) of children aged 6 to 11 years are overweight. A school nurse thinks that the percentage of 6 - to 11-year-olds who are overweight is different in her school district.

In \(1994,52 \%\) of parents with children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 256 of 800 parents with children in high school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did in 1994 ? Use the \(\alpha=0.05\) level of significance? Source: Based on "Reality Check: Are Parents and Students Ready for More Math and Science?" Public Agenda, \(2006 .\)