91Ó°ÊÓ

For their class project, a group of Statistics students decide to survey the student body to assess opinions about the proposed new student center. Their sample of 200 contained 50 first-year students, 50 sophomores, 50 juniors, and 50 seniors. a) Do you think the group was using an SRS? Why? b) What sampling design do you think they used?

For the following reports about statistical studies, identify the following items (if possible). If you can't tell, then say so-this often happens when we read about a survey. a) The population b) The population parameter of interest c) The sampling frame d) The sample e) The sampling method, including whether or not randomization was employed f) Any potential sources of bias you can detect and any problems you see in generalizing to the population of interest A company packaging snack foods maintains quality control by randomly selecting 10 cases from each day's production and weighing the bags. Then they open one bag from each case and inspect the contents.

Prior to the mayoral election discussed in Exercise 15, the newspaper also conducted a poll. The paper surveyed a random sample of registered voters stratified by political party, age, sex, and area of residence. This poll predicted that Amabo would win the election with \(52 \%\) of the vote. The newspaper was wrong: Amabo lost, getting only \(46 \%\) of the vote. Do you think the newspaper's faulty prediction is more likely to be a result of bias or sampling error? Explain.

For your political science class, you'd like to take a survey from a sample of all the Catholic Church members in your city. A list of churches shows 17 Catholic churches within the city limits. Rather than try to obtain a list of all members of all these churches, you decide to pick 3 churches at random. For those churches, you'll ask to get a list of all current members and contact 100 members at random. a) What kind of design have you used? b) What could go wrong with vour desion?

Sammy's Salsa, a small local company, produces 20 cases of salsa a day. Each case contains 12 jars and is imprinted with a code indicating the date and batch number. To help maintain consistency, at the end of each day, Sammy selects three jars of salsa, weighs the contents, and tastes the product. Help Sammy select the sample jars. Today's cases are coded 07N61 through \(07 \mathrm{~N} 80 .\) a) Carefully explain your sampling strategy. b) Show how to use random numbers to pick 3 jars. c) Did you use a simple random sample? Explain.

Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. a) We want to know what percentage of local doctors accept Medicaid patients. We call the offices of 50 doctors randomly selected from local Yellow Page listings. b) We want to know what percentage of local businesses anticipate hiring additional employees in the upcoming month. We randomly select a page in the Yellow Pages and call every business listed there.