Big Ideas Math Algebra 2, 2014
BI
Big Ideas Math Algebra 2, 2014 View details
3. Collecting Data
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Exercise 10 Page 614

A bias is an error that results in a misrepresentation of a whole population.

See solution.

Practice makes perfect

A sportswriter wants to determine whether baseball coaches think wooden bats should be mandatory in collegiate baseball. The sportswriter mails surveys to all collegiate coaches and uses the surveys that are returned. Here, the population consists of all collegiate coaches and the sample of the coaches who responded the mail. Let's recall that samples can be classified.

Name Characteristic
Random Sample Each member of the population has an equal chance of being selected.
Self-selected Sample Members volunteer to be included in the sample.
Systematic Sample Members are selected according to a specified interval from a random starting point.
Stratified Sample The population is first divided into smaller groups that share a similar characteristic. Members are then randomly selected from each group.
Cluster Sample The population is first divided into groups called clusters. All of the members in one or more of the clusters are selected.
Convenience Sample Members that are readily available or easy to reach are selected.

Even though the sportswriter mails surveys to all collegiate coaches, they only use the surveys that are returned. Therefore, this is a self-selected sample. The sample is biased because only the collegiate coaches with a strong opinion are likely to complete and return the survey.