SECTION 1.3 Data Collection and Experimental Design 23 • Systematic Sample A systematic sample is a sample in which each member of the population is assigned a number. The members of the population are ordered in some way, a starting number is randomly selected, and then sample members are selected at regular intervals from the starting number. (For instance, every 3rd, 5th, or 100th member is selected.) For instance, to collect a systematic sample of the number of people who live in West Ridge County households, you could assign a different number to each household, randomly choose a starting number, select every 100th household, and count the number of people living in each. An advantage of systematic sampling is that it is easy to use. In the case of any regularly occurring pattern in the data, however, this type of sampling should be avoided. 85 86 86 + 100 Randomly choose a starting number Select every 100th household 186 + 100 286 + 100 386 + 100 87 185 186 187 285 286 287 385 386 387 485 486 487 ... ... ... ... ... ... Systematic Sampling A type of sample that often leads to biased studies (so it is not recommended) is a convenience sample. A convenience sample consists only of members of the population that are easy to access. Identifying Sampling Techniques You are doing a study to determine the opinions of students at your school regarding stem cell research. Identify the sampling technique you are using when you select the samples listed. Discuss potential sources of bias (if any). 1. You divide the student population with respect to majors and randomly select and question some students in each major. 2. You assign each student a number and generate random numbers. You then question each student whose number is randomly selected. 3. You select students who are in your biology class. SOLUTION 1. Because students are divided into strata (majors) and a sample is selected from each major, this is a stratified sample. 2. Each sample of the same size has an equal chance of being selected and each student has an equal chance of being selected, so this is a simple random sample. 3. Because the sample is taken from students who are readily available, this is a convenience sample. The sample may be biased because biology students may be more familiar with stem cell research than other students and may have stronger opinions. TRY IT YOURSELF 4 You want to determine the opinions of students regarding stem cell research. Identify the sampling technique you are using when you select these samples. 1. You select a class at random and question each student in the class. 2. You assign each student a number and, after choosing a starting number, question every 25th student. Answer: Page A35 EXAMPLE 4 Picturing the World The research firm Gallup conducts many polls (or surveys) regarding the president, Congress, and political and nonpolitical issues. A commonly cited Gallup poll is the public approval rating of the president. For instance, the approval ratings for President DonaldTrump for selected months in 2020 are shown in the figure. (Each rating is from the poll conducted at the end of the indicated month.) 10 20 30 40 50 60 Oct Jul Apr Month Percent approving Jan President’s Approval Ratings, 2020 49 46 41 49 Discuss some ways that Gallup could select a biased sample to conduct a poll. How could Gallup select a sample that is unbiased?
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