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Sampling Situations and Bias

In each of Exercises A-D (see below), briefly identify the population (what is the basic unit and which units fall in the population?), the variables measured (what is the information desired?), and the sample. If the situation is not described in enough detail to identify the population completely, complete the description of the population in a reasonable way. Be sure that from your description it is possible to tell exactly when a unit is in the population and when it is not.

Moreover, each sampling situation described in Exercises A-D (see below) contains a serious source of probable bias. In each case, state the reason you suspect that bias will occur and also the direction of the likely bias. (That is, in what way will the sample conclusions probably differ from the truth about the population?)

A. A member of Congress in interested in whether constituents favor a proposed gun control bill. His staff reports that letters on the bill have been received from 361 constituents and that 283 of these oppose the bill.

B. A national newspaper wanted Iowa's reaction to President Bush's agricultural policy in early 1990. A reporter interviewed the first 50 persons willing to give their views, all in a single voting precinct. The headline on the resulting article read "Bush Policies Disenchant Iowa," and the reporter wrote that Bush would lose an election in Iowa if one were held then.

C. A flour company wants to know what fraction of Minneapolis households bake some or all of their own bread. A sample of 500 residential addresses is taken, and interviewers are sent to these addresses. The interviewers are employed during regular working hours on weekdays and interview only during those hours.

D. The Miami Police Department wants to know how black residents of Miami feel about police service. A questionnaire with several questions about the police is prepared. A sample of 300 mailing addresses in predominantly black neighborhoods is chosen, and a police officer is sent to each address to administer the questionnaire to an adult living there

Solution Preview

A. A member of Congress in interested in whether constituents favor a proposed gun control bill. His staff reports that letters on the bill have been received from 361 constituents and that 283 of these oppose the bill.

Population: constituents in the congressional district (a person is in the population if they live in the district; they're not in the population if they don't).

Variable: proportion of constituents that favor the gun control bill.

Sample: the 361 people who sent letters.

Probable bias: this is a self-selected sample. The sample was not randomly selected; instead, people with the strongest opinions on the issue are more likely to send in a letter (it seems as if these people are very against the bill).

B. A national newspaper wanted Iowa's reaction to President Bush's agricultural policy in early 1990. A reporter ...

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