FAST Hypothesis Testing 2 — Questions and Answers
Question 1: A researcher sets α = 0.01 instead of 0.05. What is the effect on the probability of a Type I error?
- It increases
- It decreases (Correct answer)
- It stays the same
- It doubles
Correct answer: It decreases
The significance level α directly equals the probability of a Type I error, so lowering α from 0.05 to 0.01 reduces Type I error risk.
Question 2: A study finds p = 0.03 with α = 0.05. Which conclusion is correct?
- Fail to reject H₀
- Reject H₀ (Correct answer)
- Accept H₀ as true
- The result is inconclusive
Correct answer: Reject H₀
Since p (0.03) < α (0.05), there is sufficient evidence to reject the null hypothesis.
Question 3: Which of the following best describes a one-tailed test?
- Tests for a difference in either direction
- Tests for a difference in only one specified direction (Correct answer)
- Requires a larger sample than a two-tailed test
- Is always more accurate than a two-tailed test
Correct answer: Tests for a difference in only one specified direction
A one-tailed test places the entire rejection region on one side, testing for an effect in one specified direction only.
Question 4: What does it mean when a result is statistically significant?
- The effect size is large
- The result is practically important
- The probability of obtaining the result by chance alone is below α (Correct answer)
- The null hypothesis is proven false
Correct answer: The probability of obtaining the result by chance alone is below α
Statistical significance means the observed result is unlikely (probability < α) under the assumption that H₀ is true.
Question 5: A test statistic falls in the critical region. What happens?
- H₀ is accepted
- H₀ is rejected (Correct answer)
- The sample size must be increased
- The alternative hypothesis is proven
Correct answer: H₀ is rejected
When the test statistic falls in the critical region, the result is significant and H₀ is rejected.
Question 6: Which scenario illustrates a Type II error?
- Concluding a drug works when it does not
- Concluding a drug does not work when it actually does (Correct answer)
- Setting α too high
- Choosing the wrong test statistic
Correct answer: Concluding a drug does not work when it actually does
A Type II error (β) occurs when you fail to reject a false null hypothesis — missing a real effect.
Question 7: What is the relationship between Type II error rate (β) and statistical power?
- Power = β
- Power = 1 − β (Correct answer)
- Power = α − β
- Power = α + β
Correct answer: Power = 1 − β
Statistical power is defined as 1 − β, representing the probability of correctly rejecting a false null hypothesis.
FAST Hypothesis Testing 2
A researcher sets α = 0.01 instead of 0.05.
What is the effect on the probability of a Type I error?