The management company of a local mall with 21 stores plans to survey 3 of the stores to determine the hours they would like to stay open during the holiday season. Describe how to select an SRS of 3 stores using a random number generator.

What percent of U.S. households with children have a stay-at-home parent? Phone numbers were selected at random between 8 A.M. and 5 P.M. using random-digit dialing. Explain how nonresponse might lead to bias in this study. Is the percent from the sample likely greater than or less than the percent for all U.S. households with children?

The table shows the percentage of children in the United States whose parents are college graduates in one-parent households and two-parent households. Use the information shown to solve each exercise.

$$\begin{array}{c} \text{Percentage of U.S. Children}\\ \text{whose Parents are College graduates}\\ \end{array}$$

$$\begin{array}{|c|c|} \hline 9\% & 29\%\\ \text{In One-Parent Households} & \text{In Two-Parent Households}\\ \hline \end{array}$$

$\textbf{a.}\hspace{10pt}$ What are the odds in favor of a child in a two-parent household having parents who are college graduates?

$\textbf{b.}\hspace{10pt}$ What are the odds against a child in a two-parent household having parents who are college graduates?

Suppose an SAT preparation course makes the following statement in their advertising brochure: "We asked our graduates to report on their SAT scores before and after taking our course. The mean increase in SAT scores for the 500 graduates who responded was 210 points." Describe how nonresponse might lead to bias in this study. Is the mean of 210 points likely greater than or less than the actual mean increase for all graduates of the course?

The table shows the percentage of children in the United States whose parents are college graduates in one-parent households and two-parent households. Use the information shown to solve each exercise.

$$\begin{array}{c} \text{Percentage of U.S. Children}\\ \text{whose Parents are College graduates}\\ \end{array}$$

$$\begin{array}{|c|c|} \hline 9\% & 29\%\\ \text{In One-Parent Households} & \text{In Two-Parent Households}\\ \hline \end{array}$$

$\textbf{a.}\hspace{10pt}$ What are the odds in favor of a child in a one-parent household having a parent who is a college graduate?

$\textbf{b.}\hspace{10pt}$ What are the odds against a child in a one-parent household having a parent who is a college graduate?

The manager of a home improvement store wants to know the percent of residents in his town who mow their own lawns. To find out, he selects a random sample of 100 customers and asks each one if he or she mows the lawn. Describe how undercoverage might lead to bias in this study. Explain the likely direction of the bias.

The manager of a home improvement store wishes to estimate the mean amount of money spent in the store. The estimate is to be within $4.00 with a 95 percent level of confidence. The manager does not know the standard deviation of the amounts spent. However, he does estimate that the range is from$5.00 up to $155.00. How large of a sample is needed?

The director of student life at a university wants to know what percent of students eat regularly on campus. To find out, the director selects a random sample of 300 students who live in the dorms. Explain how undercoverage might lead to bias in this study. Is the percent from the sample likely greater than or less than the percent for all students?

Norb and Gary are entered in a local golf tournament. Both have played the local course many times. Their scores are random variables with the following means and standard deviations.

$$\text { Norb, } x_{1}: \mu_{1}=115 ; \sigma_{1}=12 \quad \text { Gary, } x_{2}: \mu_{2}=100 ; \sigma_{2}=8$$

In the tournament, Norb and Gary are not playing together, and we will assume their scores vary independently of each other. The difference between their scores is $W=x_{1}-x_{2} .$ Compute the mean, variance, and standard deviation for the random variable W.

The director of student life at a university wants to know what percent of students eat regularly on campus. To find out, the director selects an SRS of 300 students who live in the dorms. Describe how undercoverage might lead to bias in this study. Explain the likely direction of the bias.

The table presents data on the elevation (in feet) and average January temperature (in degrees Fahrenheit) for 10 cities and towns in Colorado.$^{14}$ Make a scatterplot to show the relationship between elevation and average temperature in January.

Describe each of the following sampling methods and indicate conditions under which each is appropriate. a. Systematic random sampling, b. Cluster sampling, c. Stratified random sampling with proportional allocation.

In 2016, Britain's Natural Environment Research Council invited the public to name its new $300 million polar research ship. To vote on the name, people simply needed to visit a website and record their choice. Ignoring names suggested by the council, more than 124,000 people voted for "Boaty McBoatface," which ended up having more than 3 times as many votes as the second-place finisher. Explain why this sampling method is biased. Is the proportion who voted for Boaty McBoatface in the sample likely greater than or less than the proportion of all British residents who prefer the name Boaty McBoatface?

The band director at a high school wants to know what percentage of parents supports a decrease in the budget for fine arts. Because many parents attend the school's annual musical, the director surveys the first 30 parents who arrive at the show. Explain why this sampling method is biased. Is the proportion of parents in the sample who support the decrease likely greater than or less than the proportion of all parents in the school who support the decrease?