6 Chapter 1 Basic Ideas EXAMPLE 1.7 Drawing a stratified sample A company has 1000 employees, of whom 800 are full-time and 200 are part-time. The company wants to survey 50 employees about their opinions regarding benefits. Attitudes toward benefits may differ considerably between full-time and part-time employees. Why might it be a good idea to draw a stratified sample? Describe how one might be drawn. Solution If a simple random sample is drawn from the entire population of 1000 employees, it is possible that the sample will contain only a few part-time employees, and their attitudes will not be well represented. For this reason, it might be advantageous to draw a stratified sample. To draw a stratified sample, one would use two strata. One stratum would consist of the full-time employees, and the other would consist of the part-time employees. A simple random sample would be drawn from the full-time employees, and another simple random sample would be drawn from the part-time employees. This method guarantees that both full-time and part-time employees will be well represented. Explain It Again Example of a cluster sample: Imagine drawing a simple random sample of households, and interviewing every member of each household. This would be a cluster sample, with the households as the clusters. Cluster sampling In cluster sampling, items are drawn from the population in groups, or clusters. Cluster sampling is useful when the population is too large and spread out for simple random sampling to be feasible. Cluster sampling is used extensively by U.S. government agencies in sampling the U.S. population to measure sociological factors such as income and unemployment. EXAMPLE 1.8 Drawing a cluster sample To estimate the unemployment rate in a county, a government agency draws a simple random sample of households in the county. Someone visits each household and asks how many adults live in the household, and how many of them are unemployed. What are the clusters? Why is this a cluster sample? Solution The clusters are the groups of adults in each of the households in the county. This a cluster sample because a simple random sample of clusters is selected, and every individual in each selected cluster is part of the sample. Explain It Again The difference between cluster sampling and stratified sampling: In both cluster sampling and stratified sampling, the population is divided into groups. In stratified sampling, a simple random sample is chosen from each group. In cluster sampling, a random sample of groups is chosen, and every member of the chosen groups is sampled. Systematic sampling Imagine walking alongside a line of people and choosing every third one. That would produce a systematic sample. In a systematic sample, the population items are ordered. It is decided how frequently to sample items; for example, one could sample every third item, or every fifth item, or every hundredth item. Let k represent the sampling frequency. To begin the sampling, choose a starting place at random. Select the item in the starting place, along with every kth item after that. Systematic sampling is sometimes used to sample products as they come off an assembly line, in order to check that they meet quality standards. EXAMPLE 1.9 Describe a systematic sample Automobiles are coming off an assembly line. It is decided to draw a systematic sample for a detailed check of the steering system. The starting point will be the third car, then every fifth car after that will be sampled. Which cars will be sampled?
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