Investigative Questions (College Board AP® Statistics): Study Guide

Investigative questions

What is an investigative question?

• An investigative question is the question that a statistical study is designed to answer

• It is the starting point of the whole statistical process

  • Every choice made later (how to collect data, what to calculate, what to conclude) flows from the investigative question

• For example, an investigative question might be

  • "What is the mean daily screen time for teenagers aged 13 to 17 in this country?"

  • "Is there a difference between the proportion of male and female voters who support Candidate A in this state?"

What makes an investigative question valid?

• A valid investigative question for a specific study should have a defined purpose

• It should be clearly stated before any data are collected

  • It should not be changed based on the data analysis or results

• A valid investigative question should be answerable

• It should be posed so that the data needed to answer it can actually be collected and analyzed

  • An investigative question that requires data that cannot be collected (e.g. data about events that have not happened yet, or data that no one would ever truthfully report) is not a valid investigative question

What are the three components of a valid investigative question?

• A valid investigative question for an AP-style problem has three components that together guide the entire study

  1. The variables of interest

  2. The parameter and the direction of the alternative (or the goal of estimation, for a confidence interval)

  3. The population to which conclusions will apply

• Each component plays a different role in the study

  • The first guides data collection

  • The second guides data analysis

  • The third guides the conclusion that can be drawn

What is the first component (variables of interest)?

• The investigative question should be phrased in terms of the variable(s) of interest in the study

  • These are the variables that the researcher will actually measure or record

• The first component should make clear what data will need to be collected

• For example, if a researcher wants to compare the average daily commute time for adults in two different cities, the variables of interest are

  • the two cities (the categorical variable)

  • the daily commute time, in minutes (the quantitative variable)

What is the second component (parameter and direction)?

• The second component guides the type of analysis that will be performed

• For a hypothesis test, the investigative question should make clear

  • the parameter being investigated (e.g. a population mean, a population proportion, a difference between two means)

  • the direction of the alternative hypothesis such as one of the following:

    • not equal to (a two-sided test)

    • greater than (a one-sided test)

    • less than (a one-sided test)

    • association (for a chi-square test of independence)

    • not independent (for a chi-square test of independence)

• For a confidence interval, the investigative question should make clear

  • the parameter being estimated

  • the goal of estimation (e.g. estimating the parameter within a range of potential values)

What is the third component (the population)?

• The investigative question should indicate the population to which the conclusions of the study will apply

• This is the same population from which the sample is selected

• The population should be described in specific terms

  • not vague terms such as "everyone" or "people"

• For an experiment that uses random assignment of treatments, the third component should also indicate that a cause-and-effect conclusion is possible