Comparing Two Populations · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Two groups, one clear comparison

Mathematics · Data & Statistics · ages 21-22
Name ______________________   Date ____________

  1. Two sample means are twelve and seven. What is the point estimate of the difference?

    Answer: ______________

  2. Blood pressure is measured on the same patients before and after treatment. Which design is this?

    • Independent samples
    • Paired
    • One sample
    • ANOVA with five groups

  3. Blood pressure is measured on the same patients before and after treatment. Which design is this?

    • Independent samples
    • Paired
    • Single sample

  4. In a paired analysis you reduce each pair to one difference and analyse those differences.

    Circle one:   True   False

  5. The estimated difference is six with standard error two. What is the t statistic?

    Answer: ______________

  6. Why does a good pairing sharpen a comparison?

    • Shared quirks cancel in the differences
    • It removes the need for random sampling
    • It adds more subjects

  7. A 95 percent interval for the difference of means is (1, 5). What does it say?

    • Plausible differences run from 1 to 5, excluding 0, so a real difference is supported
    • 95 percent of the data lies between 1 and 5
    • The true difference is exactly 3
    • There is no difference between the groups

  8. Pairing is free: it never costs degrees of freedom and a bad match cannot hurt. True or false?

    Circle one:   True   False

  9. A researcher pairs subjects by a trait unrelated to the outcome. What is the likely result?

    • Sharper inference at no cost
    • More noise and fewer degrees of freedom
    • A guaranteed smaller p value

  10. When must you use independent samples instead of pairing?

    • When the sample size is large
    • When you want extra statistical power
    • When the two groups hold different subjects with no natural pairing
    • When measurements are expensive to collect
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Two groups, one clear comparison W1-mt_v34rZkMfqr-s1

  1. 5 · Twelve minus seven is five.
  2. Paired · Same subjects measured twice give natural pairs.
  3. Paired · The same subjects measured twice give natural pairs.
  4. True · Pairing turns each pair into a single change, and the test runs on those changes alone.
  5. 3 · Six divided by two is three.
  6. Shared quirks cancel in the differences · Subtracting within each pair wipes out subject to subject variation before it can pollute the result.
  7. Plausible differences run from 1 to 5, excluding 0, so a real difference is supported · Zero outside the interval means the data support a genuine difference.
  8. False · False. Pairs consume observations, and poor matching adds noise.
  9. More noise and fewer degrees of freedom · A weak pairing adds noise while still charging the price in lost observations.
  10. When the two groups hold different subjects with no natural pairing · No pairs means no pairing analysis. Design follows the data structure.
Worksheet · LightMySky