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Popula'on Sample Collect data from a representative Sample ... Make an Inference about the Population.
Ex. Describe the population and the sample. For each of the following situations, describe the population and the sample. (a) A survey of 17,096 students in U.S. four-year colleges reported that 19.4% were binge drinkers. Population: college students. Sample: 17,096 students. (b) In a study of work stress, 100 female restaurant workers were asked about the impact of work stress on their personal lives. Population: female restaurant workers. Sample: 100 workers. (c) A tract of forest has 584 longleaf pine trees. The diameters of 40 of these trees were measured. Population: longleaf pine trees. Sample: 584 trees.
5 How to Sample Badly
Ex. A sample of mall shoppers is fast and cheap. But people at shopping malls tend to be more prosperous than typical Americans. They are also more likely to be teenagers or retired. Moreover, unless interviewers are carefully trained, they tend to question well-dressed, respectable-looking people and avoid poorly dressed or tough-looking individuals. In short, mall interviews will not contact a sample that is representative of the entire population. Interviews at shopping malls will almost always overrepresent middle- class and retired people and underrepresent the poor. This is bias : the outcomes of mall surveys will repeatedly miss the truth about the population in the same ways.
Suppose, for example, that a news show asks viewers to participate in an on-line poll. This would be a voluntary sample. The sample is chosen by the viewers, not by the survey administrator. Voluntary response samples are always biased: they only include people who choose volunteer, where as a random sample would need to include people whether or not they choose to volunteer. Often, voluntary response samples oversample people who have strong opinions and undersample people who don't care much about the topic of the survey.
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11 How to Choose a SRS
Table B at the back of the book is a table of random digits. To make the table easier to read, the digits appear in groups of five and in numbered rows. The groups and rows have no meaning — the table is just a long list of randomly chosen digits.
The walk to your statistics class takes about 10 minutes, about the amount of time needed to listen to three songs on your iPod. You decide to take a simple random sample of songs from a Billboard list of Rock Songs. Here is the list: Select the three songs for your iPod using a simple random sample. Line #104 in the Table B:
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We need an accurate and complete list of the population. Because such a list is rarely available, most samples suffer from some degree of undercoverage. Ex. A sample survey of households, for example, will miss not only homeless people but prison inmates and students in dormitories. Ex. An opinion poll conducted by calling landline telephone numbers will miss households that have only cell phones as well as households without a phone. The results of national sample surveys therefore have some bias if the people not covered differ from the rest of the population.
A more serious source of bias in most sample surveys is nonresponse , which occurs when a selected individual cannot be contacted or refuses to cooperate. Ex. Nonresponse to sample surveys often exceeds 50%, even with careful planning and several callbacks. If the people contacted differ from those who are rarely at home or who refuse to answer questions, some bias remains. Most national sample surveys are carried out by telephone, using random digit dialing to choose residential telephone numbers at random. Call screening is increasing nonresponse to such surveys, and the rise of cell-phone-only households is increasing undercoverage.
The wording of questions wording effects is the most important influence on the answers given to a sample survey. Confusing or leading questions can introduce strong bias, and changes in wording can greatly change a survey’s outcome. Even the order in which questions are asked matters. Ex. Ask a sample of college students these two questions: “How happy are you with your life in general?” (Answers on a scale of 1 to 5) “How many dates did you have last month?” The correlation between answers is r = −0.012 when asked in this order. It appears that dating has little to do with happiness. Reverse the order of the questions, however, and r = 0.66. Asking a question that brings dating to mind makes dating success a big factor in happiness.
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