Big Ideas Math Algebra 2, 2014
BI
Big Ideas Math Algebra 2, 2014 View details
3. Collecting Data
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Exercise 40 Page 616

Practice makes perfect
a Let's start by listing all four methods of collecting data.
Method Description
Experiment We impose a treatment on individuals to collect data on their response to the treatment.
Observational Study We observe individuals and measure variables without controlling the individuals or their environment.
Survey We ask sample members one or more questions to investigate at least one characteristic of a population.
Simulation We use a model to reproduce the conditions of a situation so that the simulated outcomes match the real-world outcomes.

In our case, an airline wants to know whether travelers have enough leg room on its planes. Looking at the above list, it seems like a survey will be the most appropriate for this situation because we are interested in people's opinions.

b Now we would like to describe a sampling method that is likely to give biased results. Before we do that, let's review all of the sampling methods we know.
Type of Sample Description
Self-Selected Sample Members of a population volunteer to be in the sample.
Systematic Sample Members of a population are selected according to a particular rule.
Convenience Sample Members of a population who are easy to reach are selected.
Stratified Sample We divide the population into groups that share similar characteristics, and then members are randomly selected from each group.
Cluster Sample We divide the population into groups randomly and then members in one or more of the groups (clusters) are selected.

If we would choose self-selected sampling, we can suspect people that are not satisfied with leg room will be more likely to volunteer to be in the sample. Therefore, this method is likely to give biased results.

c If we want to obtain unbiased results we can use a systematic sampling. To do so, we could ask every 10th passenger on their opinions about the leg room in the plane.

d Finally, we want to write two questions that will fit the situation: one biased and one unbiased. To do so, let's recall the possible sources of bias.
  • Questions encourage a particular response.
  • Questions are too sensitive to answer truthfully.
  • Questions address more than one issue.
  • Questions do not provide enough information to give an accurate opinion.Now let's think of an example of a biased question.

    Do you agree that there is enough leg room for a normal passenger?

    The above question is biased because it encourages a particular response and can make respondents think that if they do not agree they are not normal. Therefore, we should always avoid these type of questions. Now let's try to formulate an unbiased question.

    Are you satisfied with the leg room on this plane?

    Notice that this is only an example solution, because we can think of multiple ways to formulate biased and unbiased questions for this situation.