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Statistical Bias

Statistical Bias#

A.P. Exam Practice#

  1. 2008, Free Response, #2

A local school board plans to conduct a survey of parents’ opinions about year-round schooling in elementary schools. The school board obtains a list of all families in the district with at least one child in an elementary school and sends the survey to a random sample of 500 of the families. The survey question is provided below.

A proposal has been submitted that would require students in elementary schools to attend school on a year- round basis. Do you support this proposal? (Yes or No)

The school board received responses from 98 of the families, with 76 of the responses indicating support for year-round schools. Based on this outcome, the local school board concludes that most of the families with at least one child in elementary school prefer year-round schooling.

  1. What is a possible consequence of nonresponse bias for interpreting the results of this survey?

  2. Someone advised the local school board to take an additional random sample of 500 families and to use the combined results to make their decision. Would this be a suitable solution to the issue raised in part a ? Explain.

  3. Suggest a different follow-up step from the one suggested in part (b) that the local school board could take to address the issue raised in part a.

  1. 2004, Free Response, Form B, #2

At a certain university, students who live in the dormitories eat at a common dining hall. Recently, some students have been complaining about the quality of the food served there. The dining hall manager decided to do a survey to estimate the proportion of students living in the dormitories who think that the quality of the food should be improved. One evening, the manager asked the first 100 students entering the dining hall to answer the following question.

Many students believe that the food served in the dining hall needs improvement. Do you think that the quality of food served here needs improvement, even though that would increase the cost of the meal plan?

  • Yes

  • No

  • No Opinion

Use this information to answer the following questions,

  1. In this setting, explain how bias may have been introduced based on the way this convenience sample was selected and suggest how the sample could have been selected differently to avoid that bias.

  2. In this setting, explain how bias may have been introduced based on the way the question was worded and suggest how it could have been worded differently to avoid that bias.

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