Chapter 2 HW: Samples, Good and Bad

In July 2018, Green Car Reports conducted a Twitter poll and asked their readers, "Which modern electric car will be the first classic?" Of the 466 people who responded to the poll, 48% chose the Tesla Roadster. (a) What is the sample size for this poll? (b) Explain why the poll may give unreliable information.

(a) 466 (b) A poll given over Twitter is a voluntary response sample and is likely to be biased.

You want to choose an SRS of 20 of Indiana's 5341 voting precincts for special voting-fraud surveillance on election day. (a) To choose an SRS, how many digits would you need to make up each of your labels for the 5341 precincts? (b) Use the table at line 107 to choose the SRS, and list the first four labels of the precincts you selected.

(a) number of digits: 4 (b) precincts 94, 3831, 4893, and 720

A university has 30000 undergraduate and 10000 graduate students. A survey of student opinion concerning health care benefits for domestic partners of students selects 300 of the 30000 undergraduate students at random and then separately selects 100 of the 10000 graduate students at random. The 400 students chosen make up the sample. Explain why this sampling method gives each student an equal chance to be chosen. Is this a simple random sample (SRS)? Select the correct statement about the resulting sample of students.

Each undergraduate has a 300/30000=1/100 chance of being selected and each graduate student has a 100/10000=1/100 chance of being selected. Since only samples with 300 undergraduates and 100 graduate students are possible, this is not an SRS.

I plan to take a sample of 10 students in my introductory statistics class. Which of the following is a simple random sample?

I write the names of all the students on similar slips of paper, put the slips of paper in a box, mix them well, and draw 10 slips from the box. The 10 names drawn are my sample.

Most sample surveys call residential telephone numbers at random. They do not, however, always ask their questions of the person who picks up the phone. Instead, they ask about the adults who live in the residence and choose one at random to be in the sample. Why is this a good idea? Select the correct explanation.

If people who answer the phone at the house are different from those who do not, the sample may be biased.

A firm wants to understand the attitudes of its managers toward its system for assessing employee performance. The list of all 32 of the firm's managers is provided. Use Table A to choose five to be interviewed in detail about the performance appraisal system. Begin at line 132 to choose the five managers. Use labels 00 to 31. Label the managers in alphabetical order.

Managers to be interviewed: Lukaku McTominay Rojo Smalling Young

A national survey of TV network news viewers found that 48% said they would believe a phone‑in poll of 300,000 persons over a random sample of 1000 persons. Of the viewers, 42% said they would believe the random sample poll. Explain to someone who knows no statistics which choice is the better guide to what all people think.

People who feel strongly about a topic are more likely to respond to a phone‑in poll in order to voice their feelings. Random sampling ensures a proper mix of people who feel strongly and people who do not.

Which of the following statements about the table of random digits are true? Select all true statements.

The digits 00000 are just as likely to appear as the digits 42895. Each pair of digits has chance 1/100 of being 00.

You are the president of the neighborhood civic association. A brewpub is thinking of opening a restaurant and bar in the neighborhood. You report to the members of the civic association that 9191 emails have been received on the issue, of which 7171 oppose opening the restaurant and bar. "I'm surprised that most of our residents oppose the restaurant and bar. I thought it would be quite popular," says a member of the association. Which is the most likely reason for the results of the emails to differ from the opinions of the general public?

The sample is not representative of the general thinking of the public due to voluntary response bias.

Beginning in 2017, there was a considerable interest in the Special Counsel investigation, conducted by Robert Mueller, of possible Russian interference in the 2016 presidential election. In 2018, the Drudge Report asked its readers, "Should President Trump fire Mueller?" As of August 9, 2018, 818,628 votes had been received on the poll with 76% answering Yes to the question. This sample is certainly biased, even though the sample size is large. What is the likely direction of the bias? That is, is 76% probably higher or lower than the truth about the opinions of the population of all adults in the United States?

The sampling method used is voluntary response. It is likely that those readers of the right-leaning Drudge Report feel strongly about whether President Trump should fire Robert Mueller due to their political stance. There are likely fewer readers with an opposing political stance. As a result, the 76% from the sample is likely greater than the true percentage of the population of all adults in the United States.

Choosing at random is a "fair" way to decide who gets some scarce good, in the sense that everyone has the same chance to win. But random choice is not always a good idea — sometimes we do not want to treat everyone the same because some people have a better claim. There are three different situations. Tickets. The basketball arena has 4000 student seats, and 7000 students want tickets. Livers. The list of people waiting for liver transplants is much larger than the number of available livers. Army. During the Vietnam War, young men were chosen for army service at random, by a "draft lottery". Decide if a random selection is the best way to choose a person in the given situations.

Use Random Chance: Tickets Do Not Use Random Chance: Livers Army

A method for selecting a sample is said to be biased if

it systematically favors certain outcomes.

Imagine the situation. You go to a website to access a news story. In order to access the story, you are asked to answer a brief survey. If you choose not to answer the survey, you can only access the article for a fee. This method for obtaining a sample is an example of

voluntary response sample.