Mastery Check Solutions

Show What You Know

Following six consecutive weeks of daily accidents on a major highway near Chicago, an Illinois civil engineer is investigating traffic congestion. The engineer’s first step toward addressing the issue is to determine the average speed and type of vehicles on the highway. 

To collect data, one clearly marked, fully visible police car is parked along the highway. Over one single morning rush hour, the police officer used radar to record the speed and vehicle type of every tenth vehicle that passed a designated checkpoint. The officer reported speeds were $3 - 5$ mph under the posted speed limit.

Identify the population and the sampling method used.

Population: All cars that travel on the highway
Sampling method: Systematic

Note

Q: Why did you choose that sampling method?

A: Sample: Because every 10th car is selected from the entire population at random, it is systematic sampling.

Identify the flaws and/or bias in the sampling. Make suggestions for improvement.

Sample flaws: Using a fully visible police car can be considered a flaw because it prompts people to slow down when they see it. Additionally, the sample is a single hour, and a single police officer records the vehicle types and their speeds, which could be difficult to capture accurately.

Sample improvement: Use traffic cameras or an unmarked police car to monitor vehicle speeds and types, so drivers do not change their driving behavior.

Note

There are many ways to collect a sample. It is possible to suggest another method entirely.

Unsatisfied with the initial sampling method, the civil engineer seeks additional feedback from highway drivers. A billboard on the highway encourages drivers to complete a survey after their journeys. One survey question asks, “Given the unacceptable levels of traffic congestion, how strongly do you agree that the state must immediately dedicate funding to improve the highway?”

Identify the biased wording, then rewrite the question to remove bias.

Bias wording: “unacceptable,” “how strongly do you agree,” “immediately”

Sample: What are the pros and cons of funding highway improvement? or Given the traffic, should funding be dedicated to updating the highway?

Say What You Know

In your own words, talk about what you have learned using the objectives for this lesson and your work on this page.

Note

Restate the objectives of the lesson in your own words. If you are unable to restate the lesson objectives, go back and reread the objectives and then explain them.

Determine the type of probability sampling method being used.
Identify the purpose of a study.
Describe the bias or misuse of statistics.
Write an unbiased statistical question.