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Parameters, Statistics, and Inference worksheets

Classify study stages, identify observations and parameters, reject invalid statistics, and compute sample summaries.

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Distinguish population parameters from sample observations and statistics. A statistic may depend only on observed sample values and known constants.

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Learning objective

What this activity builds

Separate observed sample information from unknown population quantities throughout the inference workflow.

Worked example

Is x-bar minus unknown mu a statistic?

No. It contains the unknown population parameter mu.

A statistic must be computable from the sample alone.

Teaching notes

Make the practice count

  • Name the population before naming its parameter.
  • Point to one concrete observation.
  • State the n-1 sample variance convention.

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Math SheetNameScoreTeacherDateParameters, Statistics, and InferenceDistinguish population parameters from sample observations and statistics. A statistic may depend only on observed sample values and known constants.1.For the sample 9, 12, 15, 18, 8, compute x-bar, the sample variance s^2 using denominator n-1, and sample SD s.Reference: Use x-bar=(sum x_i)/n and s^2=sum(x_i-x-bar)^2/(n-1). Round only final nonintegers to three decimals.2.A team graphs the sampled reaction times and reports their sample mean. Which stage is this?Reference: Collection obtains observations; description summarizes the observed sample; inference uses a sample to learn about a population.State the model or rule, show exact setup, then round only the final decimal.math-sheet.comPage 1 of 4
Math SheetNameScoreTeacherDateParameters, Statistics, and InferenceDistinguish population parameters from sample observations and statistics. A statistic may depend only on observed sample values and known constants.3.For study 3 of sampled commute times, a student proposes sum(x_i-mu)^2/n as a statistic, where mu is the unknown population mean. Is it a statistic? Give avalid replacement.Reference: A statistic cannot contain an unknown population parameter; it must be computable from observed data and known constants.4.A population consists of all seedling heights. A random sample records 12, 15, 18, 8, 11. Identify one observation, the population mean parameter mu, and thesample-mean statistic.Reference: A parameter describes the population and is typically unknown. An observation is one recorded value. A statistic is computed only from sample observations and known constants.State the model or rule, show exact setup, then round only the final decimal.math-sheet.comPage 2 of 4
Math SheetNameScoreTeacherDateParameters, Statistics, and InferenceDistinguish population parameters from sample observations and statistics. A statistic may depend only on observed sample values and known constants.5.For study 5 of sampled battery lifetimes, a student proposes sum(x_i-mu)^2/n as a statistic, where mu is the unknown population mean. Is it a statistic? Give avalid replacement.Reference: A statistic cannot contain an unknown population parameter; it must be computable from observed data and known constants.6.A population consists of all weekly sales. A random sample records 14, 17, 20, 10, 13, 16, 19. Identify one observation, the population mean parameter mu,and the sample-mean statistic.Reference: A parameter describes the population and is typically unknown. An observation is one recorded value. A statistic is computed only from sample observations and known constants.State the model or rule, show exact setup, then round only the final decimal.math-sheet.comPage 3 of 4
Math SheetNameScoreTeacherDateParameters, Statistics, and InferenceDistinguish population parameters from sample observations and statistics. A statistic may depend only on observed sample values and known constants.7.A team randomly selects 40 records and measures reaction times. Which stage is this?Reference: Collection obtains observations; description summarizes the observed sample; inference uses a sample to learn about a population.8.For the sample 16, 19, 9, 12, 15, 18, compute x-bar, the sample variance s^2 using denominator n-1, and sample SD s.Reference: Use x-bar=(sum x_i)/n and s^2=sum(x_i-x-bar)^2/(n-1). Round only final nonintegers to three decimals.State the model or rule, show exact setup, then round only the final decimal.math-sheet.comPage 4 of 4

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