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Statistics

Unit 5

Collecting Data

6 topics · 24 practice questions · Free responseNot yet reviewed

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Notes

Populations and sampling

  • The population is the whole group of interest and a sample is the part we study. A parameter describes a population and a statistic describes a sample.
  • Random methods: simple random sample, stratified (SRS within groups), cluster (randomly chosen groups, survey all), systematic (every $k$th after a random start).
  • Convenience and voluntary response samples are not random and tend to be biased.

Bias

  • Undercoverage, voluntary response, nonresponse and response bias (such as leading questions) each push results in a direction. A bigger sample does not fix bias.

Studies and experiments

  • Observational studies observe; experiments impose treatments. Only experiments with random assignment can show cause and effect.
  • Good experiments use control, random assignment, replication and often blinding. Blocks and matched pairs control known sources of variation.
  • Random sampling lets us generalize; random assignment lets us conclude cause and effect.

Topics in this unit

Each topic has its own short notes and practice.

Practice

A poll of 1,000 voters finds that $52\%$ favor a proposal. The $52\%$ is a:
A store surveys every 10th customer leaving, starting with a randomly chosen customer among the first 10. This is a:
A survey about school spirit is given only to students attending a football game. The best description of the problem is:
Researchers randomly assign 50 plants to Fertilizer A and 50 plants to Fertilizer B and compare their growth. This is:
The main purpose of random assignment in an experiment is to:
A researcher wants to generalize the results of a study to a whole population. Which feature is most important?

Free response

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Free-response question

A school wants to find out whether a new study app improves quiz scores. Sixty students volunteer to take part.

(a) Is this an observational study or an experiment? Identify the explanatory and response variables.

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It is an experiment if the school assigns the students to use the app or not. The explanatory variable is whether the student uses the app, and the response variable is the quiz score.

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(b) Describe how to use random assignment to form two groups of 30 students.

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Number the students 1 to 60. Use a random number generator to choose 30 different numbers. Those students use the app and the other 30 form the control group.

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(c) If the app group scores significantly higher, what can the school conclude? What limits the conclusion?

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Because of random assignment, the app caused the higher scores. Because the students were volunteers and not a random sample, the result may not apply to all students.

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