Back to Understand statistics as a process for inference — Problem 3 · Task Set 12

Exercises: Understand Statistics as a Process for Making Inferences

Work through each section in order. For each scenario, read carefully and use the correct vocabulary (population, parameter, sample, statistic) and notation. Explain your reasoning where a written response is asked for.

Grade 10·21 problems·~40 min·Common Core Math - HS Statistics and Probability·group·hss-ic-a-1

Work through problems with immediate feedback

Recall / Warm-Up

A random sample of 80 workers has a mean commute time of $\bar{x} = 27$ minutes. A student concludes, "So the mean commute time for all 50,000 workers is exactly 27 minutes." What is wrong with this conclusion?

Nothing — the sample mean always equals the population mean.

The sample statistic $\bar{x}$ is an estimate of the parameter $\mu$ , not the exact value of $\mu$ ; a different sample would give a different $\bar{x}$ .

The student should have used the median instead of the mean.

The sample of 80 is too small to compute any mean.