Statistics Hypothesis Testing & Inference 2 — Questions and Answers
Question 1: A 95% confidence interval for a population mean is (42, 58). What does this mean?
- We are 95% confident the true population mean falls between 42 and 58 (Correct answer)
- 95% of the data falls between 42 and 58
- There is a 95% chance the sample mean is in this interval
- The null hypothesis is rejected at the 5% level
Correct answer: We are 95% confident the true population mean falls between 42 and 58
A 95% CI means that 95% of intervals constructed this way from repeated samples would contain the true parameter.
Question 2: The chi-square test of independence is used to evaluate which type of claim?
- Whether two categorical variables are associated (Correct answer)
- Whether two means are significantly different
- Whether a distribution is normal
- Whether variance is equal between groups
Correct answer: Whether two categorical variables are associated
The chi-square test of independence tests whether there is a statistically significant association between two categorical variables.
Question 3: What happens to the width of a confidence interval as sample size increases?
- It decreases (Correct answer)
- It increases
- It remains the same
- It depends on the population mean
Correct answer: It decreases
Larger samples reduce the standard error, which narrows the confidence interval.
Question 4: Which non-parametric test is the alternative to the independent-samples t-test?
- Mann-Whitney U test (Correct answer)
- Wilcoxon signed-rank test
- Kruskal-Wallis test
- Spearman correlation
Correct answer: Mann-Whitney U test
The Mann-Whitney U test compares two independent groups using ranked data without assuming normality.
Question 5: What is the purpose of a paired t-test?
- To compare means from two related or matched samples (Correct answer)
- To compare means from two independent groups
- To test the relationship between two quantitative variables
- To compare variances between groups
Correct answer: To compare means from two related or matched samples
The paired t-test accounts for the correlation between two related measurements, such as before-and-after data.
Question 6: If a hypothesis test has β = 0.20, what is the power of the test?
- 0.80 (Correct answer)
- 0.20
- 0.05
- 0.95
Correct answer: 0.80
Power equals 1 minus the Type II error rate (β); 1 − 0.20 = 0.80.
Statistics Hypothesis Testing & Inference 2
A 95% confidence interval for a population mean is (42, 58).
What does this mean?