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State the null and alternative hypotheses for the statistical test described. Testing to see if there is evidence that a proportion is greater than 0.3 .

State the null and alternative hypotheses for the statistical test described. Testing to see if there is evidence that a mean is less than 50 .

A situation is described for a statistical test. In each case, define the relevant parameter(s) and state the null and alternative hypotheses. Testing to see if there is evidence that the proportion of people who smoke is greater for males than for females.

A situation is described for a statistical test. In each case, define the relevant parameter(s) and state the null and alternative hypotheses. Testing to see if there is evidence that a correlation between height and salary is significant (that is, different than zero ).

A situation is described for a statistical test. In each case, define the relevant parameter(s) and state the null and alternative hypotheses. Testing to see if average sales are higher in stores where customers are approached by salespeople than in stores where they aren't.

Pesticides and ADHD Are children with higher exposure to pesticides more likely to develop ADHD (attention-deficit/hyperactivity disorder)? In one study, authors measured levels of urinary dialkyl phosphate (DAP, a common pesticide) concentrations and ascertained ADHD diagnostic status (Yes/No) for 1139 children who were representative of the general US population. \(^{7}\) The subjects were divided into two groups based on high or low pesticide concentrations, and we compare the proportion with ADHD in each group. (a) Define the relevant parameter(s) and state the null and alternative hypotheses. (b) In the sample, children with high pesticide levels were more likely to be diagnosed with ADHD. Can we necessarily conclude that, in the population, children with high pesticide levels are more likely to be diagnosed with ADHD? (Whether or not we can make this generalization is, in fact, the statistical question of interest.) (c) In the study, evidence was found to support the alternative hypothesis. Explain what that means in the context of pesticide exposure and ADHD?

A reporter on cnn.com stated in July 2010 that \(95 \%\) of all court cases that go to trial result in a guilty verdict. To test the accuracy of this claim, we collect a random sample of 2000 court cases that went to trial and record the proportion that resulted in a guilty verdict. (a) What is/are the relevant parameter(s)? What sample statistic(s) is/are used to conduct the test? (b) State the null and alternative hypotheses. (c) We assess evidence by considering how likely our sample results are when \(H_{0}\) is true. What does that mean in this case?

It is well established that exercise is beneficial for our bodies. Recent studies appear to indicate that exercise can also do wonders for our brains, or, at least, the brains of mice. In a randomized experiment, one group of mice was given access to a running wheel while a second group of mice was kept sedentary. According to an article describing the study, "The brains of mice and rats that were allowed to run on wheels pulsed with vigorous, newly born neurons, and those animals then breezed through mazes and other tests of rodent IQ"9 compared to the sedentary mice. Studies are examining the reasons for these beneficial effects of exercise on rodent (and perhaps human) intelligence. High levels of BMP (bonemorphogenetic protein) in the brain seem to make stem cells less active, which makes the brain slower and less nimble. Exercise seems to reduce the level of BMP in the brain. Additionally, exercise increases a brain protein called noggin, which improves the brain's ability. Indeed, large doses of noggin turned mice into "little mouse geniuses," according to Dr. Kessler, one of the lead authors of the study. While research is ongoing in determining how strong the effects are, all evidence points to the fact that exercise is good for the brain. Several tests involving these studies are described. In each case, define the relevant parameters and state the null and alternative hypotheses. (a) Testing to see if there is evidence that mice allowed to exercise have lower levels of BMP in the brain on average than sedentary mice. (b) Testing to see if there is evidence that mice allowed to exercise have higher levels of noggin in the brain on average than sedentary mice. (c) Testing to see if there is evidence of a negative correlation between the level of BMP and the level of noggin in the brains of mice.

A taste test is conducted between two brands of diet cola, Brand \(\mathrm{A}\) and \(\mathrm{Brand} \mathrm{B},\) to determine if there is evidence that more people prefer Brand A. A total of 100 people participate in the taste test. (a) Define the relevant parameter(s) and state the null and alternative hypotheses. (b) Give an example of possible sample results that would provide strong evidence that more people prefer Brand A. (Give your results as number choosing Brand \(\mathrm{A}\) and number choosing Brand B.) (c) Give an example of possible sample results that would provide no evidence to support the claim that more people prefer Brand \(\mathrm{A}\). (d) Give an example of possible sample results for which the results would be inconclusive: the sample provides some evidence that Brand \(\mathrm{A}\) is preferred but the evidence is not strong.

Income East and West of the Mississippi For a random sample of households in the US, we record annual household income, whether the location is east or west of the Mississippi River, and number of children. We are interested in determining whether there is a difference in average household income between those east of the Mississippi and those west of the Mississippi. (a) Define the relevant parameter(s) and state the null and alternative hypotheses. (b) What statistic(s) from the sample would we use to estimate the difference?