Setting Up a Hypothesis Test · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Innocent until the data object

Mathematics · Data & Statistics · ages 17-18
Name ______________________   Date ____________
  1. A test runs at the 5 percent significance level. If H0 is true, what is the probability of rejecting it? Give your answer as a decimal.

    Answer: ______________

  2. A researcher claims the mean fill exceeds 5 ml. Which null hypothesis should the test start from?

    • the population mean equals 5
    • the population mean exceeds 5
    • the sample mean equals 5
    • the sample mean exceeds 5
  3. A researcher claims the mean fill exceeds 5 ml. Which null hypothesis should the test start from?

    • the population mean equals 5
    • the population mean exceeds 5
    • the sample mean equals 5
  4. A test runs at the 5 percent significance level. If H0 is true, what is the probability of rejecting it? Give your answer as a decimal.

    Answer: ______________

  5. A two-tailed test uses overall level 0.10. How much sits in each tail? Give your answer as a decimal.

    Answer: ______________

  6. Bottles are labelled 500 ml and H0 says the mean is 500 ml. In these words, a Type I error is what?

    • missing a real change in fill volume
    • concluding that the sample mean is 500
    • rejecting H0 even though the mean really is 500
  7. A machine is checked against the standard 20 g fill. The question is whether the mean differs from 20 in either direction. Which alternative fits?

    • mu > 20
    • mu != 20
    • mu < 20
    • the sample mean != 20
  8. The null hypothesis is the statement the test assumes true until the data argue otherwise. True or false?

    Circle one:   True   False

  9. A farmer claims his hens lay heavier eggs than the standard 60 g. Which alternative matches his claim?

    • mu > 60
    • mu < 60
    • mu = 60
  10. A farmer claims his hens lay heavier eggs than the standard 60 g. Which alternative matches his claim?

    • mu < 60
    • mu != 60
    • mu > 60
    • mu = 60
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Answer key

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

Innocent until the data object W1-mt_JmpLNHK0Nf-s1

  1. 0.05 · 0.05. The significance level is exactly the tolerated Type I error rate.
  2. the population mean equals 5 · The population mean equals 5. H0 is the neutral status quo about the population, using equals.
  3. the population mean equals 5 · H0 is the neutral equals claim about the population.
  4. 0.05 · The significance level is exactly the tolerated Type I error rate.
  5. 0.05 · 0.05. The two tails split the level evenly: 0.10/2 = 0.05.
  6. rejecting H0 even though the mean really is 500 · Type I means a false alarm: rejecting a true null.
  7. mu != 20 · mu != 20. Differs in either direction is two-tailed, and H1 uses the population mean mu.
  8. True · True. H0 is the default position; only strong evidence dislodges it.
  9. mu > 60 · Heavier points upward, giving a one-tailed test to the right.
  10. mu > 60 · mu > 60. Heavier points upward, giving a one-tailed test to the right.
Worksheet · LightMySky