Hypothesis Tests for a Mean with the t-Distribution · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Testing a claim about a mean

Mathematics · Data & Statistics · ages 20-21
Name ______________________   Date ____________

  1. A sample of 4 has mean 12 and standard deviation 4. Test the null that the mean is 10. Find the t statistic.

    Answer: ______________

  2. A sample of 4 has mean 12 and standard deviation 4. Test the null that the mean is 10. Find the t statistic.

    Answer: ______________

  3. Before collecting data, a researcher predicts a new drug lowers blood pressure. Which alternative fits?

    • Mean different from the old mean
    • Mean above the old mean
    • Mean below the old mean

  4. A one-sample t-test uses 10 observations. How many degrees of freedom apply?

    • 9
    • 10
    • 8

  5. A t-test gives t equal to 3.1 with p equal to 0.004 at the 5 percent level. The researcher rejects the null. Is that the right call?

    Circle one:   True   False

  6. A t-test gives t = 3.1 with p = 0.004 at the 5 percent level. The researcher rejects the null. Is that the right call?

    Circle one:   True   False

  7. Before collecting data, a researcher predicts a new drug lowers blood pressure. Which alternative fits?

    • Mean below the old mean (one-tailed)
    • Mean different from the old mean (two-tailed)
    • Mean above the old mean (one-tailed)
    • Mean exactly equal to the old mean

  8. A sample of 9 has mean 30 and standard deviation 6. Test the null that the mean is 24. Find the t statistic.

    Answer: ______________

  9. A study reports p equal to 0.06 at the 5 percent level and concludes the drug has no effect. What is wrong?

    • Nothing, the null is proven
    • A nonsignificant result only fails to reject; it never proves no effect
    • The level should change to fit the p-value

  10. A sample of 16 has mean 20 and standard deviation 8. Test the null that the mean is 16. Find the t statistic.

    Answer: ______________

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Answer key

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

Testing a claim about a mean W1-mt_ig2o39hAwh-s1

  1. 1 · Standard error is 4 over 2, which is 2, and the gap 12 minus 10 over 2 is 1.
  2. 1 · The gap is 2 and the standard error is 2, so the statistic is 1.
  3. Mean below the old mean · A predicted lowering is directional, so the lower tail is the right one.
  4. 9 · Degrees of freedom are one fewer than the number of observations.
  5. True · A p-value below the level rejects the null.
  6. True · Yes. The p-value sits below 0.05, so the data are surprising enough under the null to reject it.
  7. Mean below the old mean (one-tailed) · The prediction names a direction in advance, so the one-tailed below alternative matches it.
  8. 3 · The gap is 6 and the standard error is 2, so the statistic is 3.
  9. A nonsignificant result only fails to reject; it never proves no effect · Failing to reject only says the data do not contradict the null.
  10. 2 · The gap is 4 and the standard error is 2, so the statistic is 2.
Worksheet · LightMySky