Chapter 4: Collecting Data

No tipping The owner of a large restaurant is considering a new "no tipping" policy and wants to survey a sample of employees. The policy would add $20\%$ to the cost of food and beverages and the additional revenue would be distributed equally among servers and kitchen staff. Describe how to select a stratified random sample of approximately $30$ employees. Explain your choice of strata and why stratified random sampling might be preferred in this context.

The owner of a chain of supermarkets notices that there is a positive correlation between the sales of beer and the sales of ice cream over the course of the previous year. During seasons when sales of beer were above average, sales of ice cream also tended to be above average. Likewise, during seasons when sales of beer were below average, sales of ice cream also tended to be below average. Which of the following would be a valid conclusion from these facts?

a. Sales records must be in error. There should be no association between beer and ice cream sales.

b. Evidently, for a significant proportion of customers of these supermarkets, drinking beer causes a desire for ice cream or eating ice cream causes a thirst for beer.

c. A scatterplot of monthly ice cream sales versus monthly beer sales would show that a straight line describes the pattern in the plot, but it would have to be a horizontal line.

d. There is a clear negative association between beer sales and ice cream sales.

e. The positive correlation is most likely a result of the variable temperature; that is, as temperatures increase, so do both beer sales and ice cream sales.

Parking on campus The director of student life at a university wants to estimate the proportion of undergraduate students who regularly park a car on campus. Describe how to select a stratified random sample of approximately $100$students. Explain your choice of strata and why stratified random sampling might be preferred in this context.

SRS of engineers? A corporation employs $2000$ male and $500$ female engineers. A stratified random sample of $200$ male and $50$ female engineers gives every individual in the population the same chance to be chosen for the sample. Is it an SRS? Explain your answer.

Before he goes to bed each night, Mr. Kleen pours dishwasher powder into his dishwasher and turns it on. Each morning, Mrs. Kleen weighs the box of dishwasher powder. From an examination of the data, she concludes that Mr. Kleen dispenses a rather consistent amount of powder each night. Which of the following statements is

true?

I. There is a high positive correlation between the number of days that have passed since the box of dishwasher powder was opened and the amount of powder left in the box.

II. A scatterplot with days since purchase as the explanatory variable and total amount of dishwasher powder used as the response variable would display a strong positive association.

III. The correlation between the amount of powder left in the box and the amount of powder used should be $-1.$

a. I only

b. II only

c. III only

d. II and III only

e. I, II, and III

Student archaeologists An archaeological dig turns up large numbers of pottery shards,

broken stone tools, and other artifacts. Students working on the project classify each

artifact and assign a number to it. The counts in different categories are important for

understanding the site, so the project director chooses $2\%$of the artifacts at random and

checks the students’ work. Identify the population and the sample.

SRS of students? At a party, there are $30$ students over age $21$ and $20$students underage$21$. You choose at random $3$ of those over $21$ and separately choose at random $2$ of those under $21$ to interview about their attitudes toward alcohol. You have given every student at the party the same chance to be interviewed. Is your sample an SRS? Explain your answer.

How is your room? A hotel has $30$floors with $40$rooms per floor. The rooms on one side of the hotel face the water, while rooms on the other side face a golf course. There is an extra charge for the rooms with a water view. The hotel manager wants to select $120$rooms and survey the registered guest in each of the selected rooms about his or her overall satisfaction with the property.

a. Describe how to obtain a sample of $120$rooms using stratified random sampling. Explain your choice of strata and why this method might be preferred to simple random sampling.

b. Describe how to obtain a sample of $120$rooms using cluster sampling. Explain your choice of clusters and why this method might be preferred to simple random sampling.

Go Blue! Michigan Stadium, also known as "The Big House," seats over $100,000$fans for a football game. The University of Michigan Athletic Department wants to survey fans about concessions that are sold during games. Tickets are most expensive for seats on the sidelines. The cheapest seats are in the end zones (where one of the authors sat as a student). A map of the stadium is shown.

a. Describe how to obtain a sample using stratified random sampling. Explain your choice of strata and why this method might be preferred to simple random sampling.

b. Describe how to obtain a sample using cluster sampling. Explain your choice of clusters and why this method might be preferred to simple random sampling.

High-speed Internet Laying fiber-optic cable is expensive. Cable companies want to make sure that if they extend their lines to less dense suburban or rural areas, there will be sufficient demand so the work will be cost-effective. They decide to conduct a survey to determine the proportion of households in a rural subdivision that would buy the service. They select a simple random sample of $5$blocks in the subdivision and survey each family that lives on one of those blocks.

a. What is the name for this kind of sampling method?

b. Give a possible reason why the cable company chose this method.