SECTION 1.3 Data Collection and Experimental Design 21 Sampling Techniques A census is a count or measure of an entire population. Taking a census provides complete information, but it is often costly and difficult to perform. A sampling is a count or measure of part of a population and is more commonly used in statistical studies. To collect unbiased data, a researcher must ensure that the sample is representative of the population. Appropriate sampling techniques must be used to ensure that inferences about the population are valid. Remember that when a study is done with faulty data, the results are questionable. Even with the best methods of sampling, a sampling error may occur. A sampling error is the difference between the results of a sample and those of the population. When you learn about inferential statistics, you will learn techniques of controlling sampling errors. A random sample is one in which every member of the population has an equal chance of being selected. A simple random sample is a sample in which every possible sample of the same size has the same chance of being selected. One way to collect a simple random sample is to assign a different number to each member of the population and then use a random number table such as Table 1 in Appendix B. Responses, counts, or measures for members of the population whose numbers correspond to those generated using the table would be in the sample. Calculators and computer software programs are also used to generate random numbers (see page 36). Portion of Table 1 found in Appendix B Consider a study of the number of people who live in West Ridge County. To use a simple random sample to count the number of people who live in West Ridge County households, you could assign a different number to each household, use a technology tool or table of random numbers to generate a sample of numbers, and then count the number of people living in each selected household. Using a Simple Random Sample There are 731 students currently enrolled in a statistics course at your school. You wish to form a sample of eight students to answer some survey questions. Select the students who will belong to the simple random sample. SOLUTION Assign numbers 1 to 731 to the students in the course. In the table of random numbers, choose a starting place at random and read the digits in groups of three (because 731 is a three-digit number). For instance, if you started in the third row of the table at the beginning of the second column, you would group the numbers as follows: 719 66 2 738 6 50 004 053 58 9 403 1 29 281 185 44 Ignoring numbers greater than 731, the first eight numbers are 719, 662, 650, 4, 53, 589, 403, and 129. The students assigned these numbers will make up the sample. To find the sample using a TI-84 Plus, follow the instructions shown at the left. EXAMPLE 3 Study Tip A biased sample is one that is not representative of the population from which it is drawn. For instance, a sample consisting of only 18- to 22-year-old U.S. college students would not be representative of the entire 18- to 22-year-old population in the United States. Tech Tip You can use technology such as Minitab, Excel, StatCrunch, or the TI-84 Plus to generate random numbers. (Detailed instructions for using Minitab, Excel, and the TI-84 Plus are shown in the technology manuals that accompany this text.) For instance, here are instructions for using the random integer generator on a TI-84 Plus for Example 3. MATH Choose the PRB menu. 5: randInt( 1 , 7 3 1 , 8 ) ENTER randInt(1,731,8) {537 33 249 728... Continuing to press ENTER will generate more random samples of 8 integers. To explore this topic further, see Activity 1.3 on page 27. 1.3
RkJQdWJsaXNoZXIy NjM5ODQ=