DSST Statistics 3 — Questions and Answers
Question 1: A researcher wants to estimate the average height of students at a university. She randomly selects 50 students. This is an example of:
- Census
- Stratified sampling
- Simple random sampling (Correct answer)
- Systematic sampling
Correct answer: Simple random sampling
Randomly selecting individuals from the population without structured grouping is simple random sampling.
Question 2: The standard error of the mean is equal to:
- σ / n
- σ / √n (Correct answer)
- σ × √n
- σ²/ n
Correct answer: σ / √n
Standard error = σ / √n; it measures how much sample means vary around the population mean.
Question 3: Which of the following best describes a negatively skewed distribution?
- The tail extends to the right
- The mean equals the median
- The tail extends to the left (Correct answer)
- The distribution is symmetric
Correct answer: The tail extends to the left
A negatively skewed distribution has a longer tail on the left side, pulling the mean below the median.
Question 4: In a chi-square test of independence, the null hypothesis states that:
- The two variables are dependent
- The two variables are independent (Correct answer)
- The sample mean equals the population mean
- Variances are equal
Correct answer: The two variables are independent
The null hypothesis in a chi-square test of independence is that the two categorical variables are not associated.
Question 5: What does a 95% confidence interval mean?
- There is a 95% probability the parameter is in this specific interval
- 95% of the data falls within the interval
- If repeated sampling were done, 95% of such intervals would contain the true parameter (Correct answer)
- The sample statistic equals the parameter 95% of the time
Correct answer: If repeated sampling were done, 95% of such intervals would contain the true parameter
The correct frequentist interpretation is that 95% of confidence intervals constructed this way will capture the true parameter.
Question 6: Which nonparametric test is the counterpart of the independent-samples t-test?
- Wilcoxon signed-rank test
- Kruskal-Wallis test
- Mann-Whitney U test (Correct answer)
- Friedman test
Correct answer: Mann-Whitney U test
The Mann-Whitney U test compares two independent groups using rank order rather than means.
Question 7: In regression analysis, the coefficient of determination (R²) tells you:
- The slope of the regression line
- The proportion of variance in Y explained by X (Correct answer)
- Whether the regression is statistically significant
- The correlation between residuals and X
Correct answer: The proportion of variance in Y explained by X
R² ranges from 0 to 1 and represents the fraction of variance in the dependent variable accounted for by the model.
DSST Statistics 3
A researcher wants to estimate the average height of students at a university.
She randomly selects 50 students.
This is an example of: