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. Under H0, a continuous test has two disjoint rejection tails, each with probability 0.03. What is the total rejection probability?

    Answer: ______________

  2. Let p be the probability that a ticket wins. Before collecting data, a researcher plans to test whether p is below 0.2. Which H1 fits?

    • H1: p = 0.2
    • H1: p > 0.2
    • H1: p < 0.2
    • H1: sample share < 0.2

  3. A researcher tests whether the population mean fill exceeds 5 ml. Using the equality-null convention, which H0 fits?

    • The population mean is 5 ml
    • The population mean exceeds 5 ml
    • The observed sample mean is 5 ml

  4. A valid test uses a 5 percent significance level. What is the largest allowed probability of rejecting H0 when H0 is true? Give a decimal.

    Answer: ______________

  5. A valid test has significance level 0.02 and actual Type I error probability 0.012. How far below the allowed bound is its actual probability?

    Answer: ______________

  6. A bottle test uses H0: μ = 500 ml against μ ≠ 500 ml. Which outcome is a Type I error?

    • Not rejecting H0 when μ has departed from 500 ml
    • Treating a sample mean of 500 ml as proof of H0
    • Rejecting H0 when μ really equals 500 ml

  7. A researcher planned a two-tailed test. After seeing a high sample mean, she changes it to an upper-tail test. What is the problem?

    • The direction was changed after seeing the result
    • Every hypothesis test must use two equal tails
    • An upper-tail test cannot use a population mean
    • A high sample mean proves the null hypothesis

  8. With the same sample size, making a test's rejection region smaller can reduce false alarms while making a real departure easier to miss.

    Circle one:   True   False

  9. Let μ be the population mean egg mass in grams. A farmer plans to test whether it exceeds the standard 60 g. Which H1 matches?

    • μ > 60
    • μ < 60
    • μ = 60

  10. A test asks whether the population mean μ exceeds 30. Using an inclusive one-sided null, which pair covers the null and alternative sides without overlap?

    • H0: μ < 30; H1: μ > 30
    • H0: μ ≥ 30; H1: μ > 30
    • H0: μ ≤ 30; H1: μ < 30
    • H0: μ ≤ 30; H1: μ > 30
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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. 0.06 · The tails are disjoint, so add their probabilities: 0.03 + 0.03 = 0.06.
  2. H1: p < 0.2 · The population parameter is p. Below 0.2 means p < 0.2, not a statement about the observed sample share.
  3. The population mean is 5 ml · Under the stated convention, H0 fixes the population mean at 5 ml. The greater-than claim belongs in H1.
  4. 0.05 · The significance level bounds the Type I error probability by 5 / 100 = 0.05. The actual probability need not equal that bound.
  5. 0.008 · Subtract the actual probability from the bound: 0.020 - 0.012 = 0.008.
  6. Rejecting H0 when μ really equals 500 ml · A Type I error rejects a true null. Here that means reporting a departure even though the population mean is 500 ml.
  7. The direction was changed after seeing the result · The test direction must come from the planned question. Choosing it after seeing the result changes the procedure and can invalidate its stated error control.
  8. True · A smaller rejection region rejects fewer possible outcomes. This can reduce rejection under a true H0 and increase failure to reject under a false H0.
  9. μ > 60 · Exceeds means greater than, so H1 is μ > 60. The planned test uses the upper tail.
  10. H0: μ ≤ 30; H1: μ > 30 · H1 is μ > 30. Its complementary null is μ ≤ 30, which includes the boundary and all values on the other side.
Worksheet · LightMySky