Statistics Hypothesis Testing & Inference 1 — Questions and Answers
Question 1: What does the null hypothesis (H₀) typically represent in a statistical test?
- No effect or no difference exists in the population (Correct answer)
- A significant difference exists in the population
- The researcher's prediction is correct
- The sample statistic equals the parameter
Correct answer: No effect or no difference exists in the population
The null hypothesis is the default claim of no effect, no difference, or no relationship.
Question 2: What is a Type I error in hypothesis testing?
- Rejecting a true null hypothesis (Correct answer)
- Failing to reject a false null hypothesis
- Using the wrong test statistic
- Setting alpha too low
Correct answer: Rejecting a true null hypothesis
A Type I error (false positive) occurs when we reject a null hypothesis that is actually true.
Question 3: If a p-value is 0.03 and the significance level α is 0.05, what conclusion is drawn?
- Reject the null hypothesis (Correct answer)
- Fail to reject the null hypothesis
- Accept the null hypothesis
- Increase the sample size
Correct answer: Reject the null hypothesis
Since p = 0.03 < α = 0.05, there is sufficient evidence to reject the null hypothesis.
Question 4: Which test is appropriate for comparing the means of two independent groups?
- Two-sample t-test (Correct answer)
- Paired t-test
- Chi-square test
- ANOVA
Correct answer: Two-sample t-test
The two-sample (independent samples) t-test compares means from two separate, unrelated groups.
Question 5: What does statistical power represent?
- The probability of correctly rejecting a false null hypothesis (Correct answer)
- The probability of making a Type I error
- The width of a confidence interval
- The effect size of a study
Correct answer: The probability of correctly rejecting a false null hypothesis
Power is the probability of detecting a true effect (1 − β, where β is the Type II error rate).
Question 6: What is a one-tailed hypothesis test used for?
- Testing for an effect in a specific direction (Correct answer)
- Testing for any difference regardless of direction
- Comparing more than two groups
- Testing proportions only
Correct answer: Testing for an effect in a specific direction
A one-tailed test places the rejection region entirely in one tail when the research hypothesis specifies a direction.
Statistics Hypothesis Testing & Inference 1
What does the null hypothesis (H₀) typically represent in a statistical test?