Identifying Sampling Methods and Errors

1. Identifying Sampling Methods and Errors AP Statistics—used with chapter 12 BVD

2. Example #1 A principal wants survey the student body about their opinions concerning a new school board policy that restricts who can and cannot drive to school in the morning. She believes that the views of students will differ based on how the students get to school in the morning. She has identified four modes of transportation in the morning: walkers, bus riders, drivers, and those driven by parents or other non-students. Describe how the principal should conduct this survey and identify the sampling method.

3. Example #2 The NFL commissioner wants is concerned about reports that large numbers of professional football players are carrying concealed weapons in public. He would like to conduct a survey. It is financially unfeasible and he is advised to conduct a cluster sample based on team. He would like to survey 200 players and would like to have those 200 players come from 10 teams. Describe how the commissioner could conduct this survey.

4. Example #3 An accounting firm has received many complaints that one of their accountants has been making many mistakes on tax returns. This accountant has worked on over 1,000 returns, so checking each one of them for mistakes would take too long. How could the accounting firm use systematic sampling to check for errors? Describe what they should do.

5. Example #4 Your school principal has decided to grant five special “sleep in” days during the upcoming school year (180 days). He wants to select these days at random, but is not sure how to do it. Describe how he could conduct a simple random sample (SRS) to determine the 180 days. Also, describe how he could conduct a stratified sample to determine the 180 days. Which do you think is more appropriate? Why?

6. Example #5 A local political group wants to see if high school students believe that their should be a government health care option. The group sends out three different workers to get the views of the students. The workers are placed at the three different entrances to the school and they ask the students as they walk into the school if they believe a government option should be made available. Discuss the problems with the sampling method. Be specific and use proper terms

7. Example #6 In 1992, flight attendants handed out a survey to passengers who were flying from New York to Chicago on Midway Airlines. Based on the results of this survey, Midway Airlines purchased advertisements in The New York Times and the Wall Street Journal, which stated that 84% of New York to Chicago business travelers prefer Midway to American, TWA, or United Airlines. The advertisement apparently claims that 84% is a reasonable estimate of the percentage “of New York to Chicago business travelers who prefer Midway to American, TWA, or United Airlines.” Someone complained that the ad isn’t fair because most of the passengers neither filled out the survey nor returned it to the flight attendant. What kind of problem is this complaint highlighting? How does it affect the results. Use proper vocabulary.

8. Example #7 In 1992, flight attendants handed out a survey to passengers who were flying from New York to Chicago on Midway Airlines. Based on the results of this survey, Midway Airlines purchased advertisements in The New York Times and the Wall Street Journal, which stated that 84% of New York to Chicago business travelers prefer Midway to American, TWA, or United Airlines. The advertisement apparently claims that 84% is a reasonable estimate of the percentage “of New York to Chicago business travelers who prefer Midway to American, TWA, or United Airlines.” Someone complained that the ad wasn’t fair because US Air also operates between New York and Chicago and wasn’t included on the survey. What kind of problem is this complaint highlighting? How does it affect the results. Use proper vocabulary.

9. Example #8 A local radio station runs a daily question that can be answered by phone or online. One of these questions was “Do you believe that the Obama administration is doing enough to help the economy?”. Of the 670 people who responded, 450 said yes. This poll does not give a trustworthy estimate of the local populations’ views concerning how much the Obama administration is doing to help the economy . Why? Use proper vocabulary.

10. Example #9 You want to ask a sample of undergraduates at State Tech how they feel about a proposal to delay future Spring Breaks by a week. Opinions may differ depending on the class of the student, especially since the seniors will have left before the policy is changed. So you take separate SRSs of seniors and non-seniors and combine them to form you sample. This is an example of what kind of sampling method?

11. Example 10 You want to ask a sample of undergraduates at State Tech how they feel about a proposal to delay future Spring Breaks by a week. Opinions may differ depending on the class of the student, especially since the seniors will have left before the policy is changed. So you take separate SRSs of seniors and non-seniors and combine them to form you sample. The results are as follows: 72% of the non-seniors favor delaying Spring Break by a week, but only 28% of the seniors do. How would you calculate an estimate of the percentage of all State Tech undergraduates who favor delaying the break? Show your work and give an estimate.