A research firm claims that $62 \%$ of women in the 40-49 age group save in a $401(\mathrm{k})$ or individual retirement account. If we wished to test whether this percentage could be the same for women in this age group living in New York City and selected a random sample of 300 such individuals from New York, what would be the null and alternative hypotheses? Would the test be a $z$-test or a $t$-test? Why?

For each of the following statements, formulate appropriate null and alternative hypotheses. Indicate whether the appropriate test will be one-tail or twotail, then sketch a diagram that shows the approximate location of the "rejection" region(s) for the test.

d. "The average employee put in $3.5$ hours of overtime last week."

For each of the following statements, formulate appropriate null and alternative hypotheses. Indicate whether the appropriate test will be one-tail or twotail, then sketch a diagram that shows the approximate location of the "rejection" region(s) for the test.

c. "The average SAT score for entering freshmen is at least $1200 . "$

For each of the following statements, formulate appropriate null and alternative hypotheses. Indicate whether the appropriate test will be one-tail or twotail, then sketch a diagram that shows the approximate location of the "rejection" region(s) for the test.

b. "The average adult drinks $1.5$ cups of coffee per day."

For each of the following statements, formulate appropriate null and alternative hypotheses. Indicate whether the appropriate test will be one-tail or twotail, then sketch a diagram that shows the approximate location of the "rejection" region(s) for the test.

a. "The average college student spends no more than $\$ 300$ per semester at the university's bookstore."

In response to the assertion made in Exercise 10.8, suppose an insurance company executive were to claim the percentage of fraudulent auto theft reports to be "no more than $10 \%$." What null and alternative hypotheses would be appropriate in evaluating the executive's statement?

A state representative is reported as saying that about $10 \%$ of reported auto thefts involve owners whose cars have not really been stolen, but who are trying to defraud their insurance company. What null and alternative hypotheses would be appropriate in evaluating the statement made by this legislator?

Many law enforcement agencies use voice-stress analysis to help determine whether persons under interrogation are lying. If the sound frequency of a person's voice changes when asked a question, the presumption is that the person is being untruthful. For this situation, state the null and alternative hypotheses in verbal terms, then identify what would constitute a Type I error and a Type II error in this situation.

On CNN and other news networks, guests often express their opinions in rather strong, persuasive, and sometimes frightening terms. For example, a scientist who strongly believes that global warming is taking place will warn us of the dire consequences (such as rising sea levels, coastal flooding, and global climate change) she foresees if we do not take her arguments seriously. If the scientist is correct, and the world does not take her seriously, would this be a Type I error or a Type II error? Briefly explain your reasoning.

The president of a company that manufactures central home air conditioning units has told an investigative reporter that at least $85 \%$ of its homeowner customers claim to be "completely satisfied" with the overall purchase experience. If the reporter were to subject the president's statement to statistical scrutiny by questioning a sample of the company's residential customers, would the test be one-tail or two-tail? What would be the appropriate null and alternative hypotheses?

What is the difference between a null hypothesis and an alternative hypothesis? Is the null hypothesis always the same as the verbal claim or assertion that le to the test? Why or why not?

A researcher has estimated that U.S. college students spend an average of $17.2$ hours per week on the Internet. Assuming a simple random sample of $500 \mathrm{col}$ lege students and a sample standard deviation of $1.4$ hours per week, construct and interpret the $99 \%$ confidence interval for the population mean.

A truck loaded with 8000 electronic circuit boards has just pulled into a firm's receiving dock. The supplier claims that no more than $3 \%$ of the boards fall outside the most rigid level of industry performance specifications. In a simple random sample of 300 boards from this shipment, 12 fall outside these specifications. Construct the $95 \%$ confidence interval for the percentage of all boards in this shipment that fall outside the specifications, then comment on whether the supplier's claim would appear to be correct.

A researcher, believing $\pi$ to be no more than $0.40$, calculates the necessary sample size for the confidence level and maximum likely error he has specified. Upon completing the study, he finds the sample proportion to be $0.32$. Is the maximum likely error greater than, equal to, or less than that originally specified? Explain.