Answer: Correct decision, when H₀ is false. Correctly rejecting a false H₀ is the correct decision (with probability = power).

A Type I error occurs when:

Answer: We reject H₀ when H₀ is true. Type I error = rejecting a true null hypothesis (false positive). Probability = α.

Answer: α = 0.05 By construction, the significance level α equals the Type I error probability when H₀ is true.

AP Statistics · Topic 6.7

Potential Errors When Performing Tests Practice

Part of Inference for Categorical Data: Proportions.(UNC-5.A)

Practice questions

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Sample questions

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Sample 1difficulty 2/5
$A test correctly rejects H₀.$
$This corresponds to:$
- A
  $Sampling error.$
- B
  $Type I error.$
- C
  $Type II error.$
- D
  $Correct decision, when H₀ is false.$
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Why
$Correctly rejecting a false H₀ is the correct decision (with probability = power).$
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Sample 2difficulty 2/5
$A test of H₀: p = 0.5 vs Hₐ: p > 0.5.$
$A Type I error occurs when:$
- A
  $We fail to reject H₀ when H₀ is false.$
- B
  $We reject H₀ when Hₐ is true.$
- C
  $We fail to reject H₀ when H₀ is true.$
- D
  $We reject H₀ when H₀ is true.$
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Why
$Type I error = rejecting a true null hypothesis (false positive). Probability = α.$
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Sample 3difficulty 2/5
$A test is conducted at α = 0.05.$
$P(Type I error) =$
- A
  $1 - α = 0.95$
- B
  $Power$
- C
  $β$
- D
  $α = 0.05$
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Why
$By construction, the significance level α equals the Type I error probability when H₀ is true.$
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Sample 4difficulty 2/5
$A pharmaceutical company tests H₀: drug is ineffective vs Hₐ: drug is effective.$
$What is a Type II error in this context?$
- A
  $Concluding the drug is effective when it actually is effective.$
- B
  $Concluding the drug is ineffective when it actually is ineffective.$
- C
  $Concluding the drug is ineffective when it actually is effective.$
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- D
  $Concluding the drug is effective when it actually is ineffective.$
Why
$Type II error = failing to reject a false H₀. Here: failing to detect a real effect.$
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Sample 5difficulty 3/5
$A statistician decreases α from 0.05 to 0.01.$
$Decreasing α will:$
- A
  $Increase both Type I and Type II errors.$
- B
  $Have no effect on Type II error.$
- C
  $Decrease both Type I and Type II errors.$
- D
  $Decrease P(Type I error) and increase P(Type II error).$
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Why
$Smaller α means a smaller rejection region; this lowers Type I error but increases Type II error.$
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