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\- Roller coasters An amusement park has opened a new roller coaster. It is so popular that people are waiting for up to 3 hours for a 2 -minute ride. Concerned about how patrons (who paid a large amount to enter the park and ride on the rides) feel about this, they survey every 10 th person on the line for the roller coaster, starting from a randomly selected individual. a) What kind of sample is this? b) What is the sampling frame? c) Is it likely to be representative?

\- Survey questions Examine each of the following questions for possible bias. If you think the question is biased, indicate how and propose a better question. a) Should companies that pollute the environment be compelled to pay the costs of cleanup? b) Given that 18 -year-olds are old enough to vote and to serve in the military, is it fair to set the drinking age at \(21 ?\)

Phone surveys Anytime we conduct a survey, we must take care to avoid undercoverage. Suppose we plan to select 500 names from the city phone book, call their homes between noon and \(4 \mathrm{PM}\), and interview whoever answers, anticipating contacts with at least 200 people. a) Why is it difficult to use a simple random sample here? b) Describe a more convenient, but still random, sampling strategy. c) What kinds of households are likely to be included in the eventual sample of opinion? Excluded? d) Suppose, instead, that we continue calling each number, perhaps in the morning or evening, until an adult is contacted and interviewed. How does this improve the sampling design? e) Random-digit dialing machines can generate the phone calls for us. How would this improve our design? Is anyone still excluded?

\- Arm length How long is your arm compared with your hand size? Put your right thumb at your left shoulder bone, stretch your hand open wide, and extend your hand down your arm. Put your thumb at the place where your little finger is, and extend down the arm again. Repeat this a third time. Now your little finger will probably have reached the back of your left hand. If the fourth hand width goes past the end of your middle finger, turn your hand sideways and count finger widths to get there. a) How many hand and finger widths is your arm? b) Suppose you repeat your measurement 10 times and average your results. What parameter would this average estimate? What is the population? c) Suppose you now collect arm lengths measured in this way from 9 friends and average these 10 measurements. What is the population now? What parameter would this average estimate? d) Do you think these 10 arm lengths are likely to be representative of the population of arm lengths in your community? In the country? Why or why not?

Satisfied workers The managers of a large company wished to know the percentage of employees who feel "extremely satisfied" to work there. The company has roughly 24,000 employees. They contacted a random sample of employees and asked them about their job satisfaction, obtaining 437 completed responses. a) The company's annual report states, "Our survey shows that \(87.34 \%\) of our employees are "very happy" working here." Comment on that claim. Use appropriate statistics terminology. b) One manager suggested surveying employees by assigning computer-generated random numbers to each employee on a list of all employees and then contacting all those whose assigned random number is divisible by \(7 .\) Is this a simple random sample? c) For each scenario suggested by a different manager, determine the sampling method. i. Use the company e-mail directory to contact 150 cmployees from among those employed for less than 5 years, 150 from among those employed for \(5-10\) years, and 150 from among those employed for more than 10 years. ii. Use the company e-mail directory to contact every 50th employce on the list. iii. Select several divisions of the company at random. Within each division, draw an SRS of employees to contact. d) One manager suggested having the head of each corporate division hold a meeting of their employees to ask whether they are happy on their jobs. They will ask people to raise their hands to indicate whether they are happy. What problems do you see with this plan? e) For each of these designs proposed by a different manager, identify the problem with the method and the effect it would have on the estimate of the percentage of cmployees who feel "extremely satisfied" to work there. i. Leave a stack of surveys out in the employee cafeteria so people can pick them up and return them. ii. Stuff a questionnaire in the mailbox of each employee with the request that they fill it out and return it.