DSST Statistics 4 — Questions and Answers
Question 1: A fair coin is flipped 10 times. The probability of exactly 3 heads follows which distribution?
- Normal
- Poisson
- Binomial (Correct answer)
- Geometric
Correct answer: Binomial
Fixed trials, constant probability of success, and two outcomes define a binomial distribution.
Question 2: Which of the following is a characteristic of the normal distribution?
- It is skewed to the right
- Mean, median, and mode are all equal (Correct answer)
- It has two peaks
- Its tails touch the x-axis at finite values
Correct answer: Mean, median, and mode are all equal
The normal distribution is perfectly symmetric, so its mean, median, and mode coincide.
Question 3: An ANOVA test is used to compare:
- Two proportions
- Two variances
- Three or more group means (Correct answer)
- Two medians
Correct answer: Three or more group means
Analysis of Variance (ANOVA) tests whether the means of three or more groups are equal.
Question 4: Bayes' theorem is used to:
- Calculate population variance
- Update probability estimates given new evidence (Correct answer)
- Test differences between two means
- Find the regression coefficient
Correct answer: Update probability estimates given new evidence
Bayes' theorem allows you to revise a prior probability in light of new data to get a posterior probability.
Question 5: Which of the following sampling methods divides the population into subgroups and samples from each?
- Cluster sampling
- Convenience sampling
- Stratified sampling (Correct answer)
- Systematic sampling
Correct answer: Stratified sampling
Stratified sampling splits the population into strata (subgroups) and draws random samples from each.
Question 6: The p-value in a hypothesis test represents:
- The probability that the null hypothesis is true
- The probability of observing results at least as extreme as the data, assuming H₀ is true (Correct answer)
- The power of the test
- One minus the confidence level
Correct answer: The probability of observing results at least as extreme as the data, assuming H₀ is true
The p-value is the probability of getting results as extreme as or more extreme than observed, given that H₀ is true.
Question 7: A box-and-whisker plot displays which five summary statistics?
- Mean, SD, variance, skewness, kurtosis
- Min, Q1, Median, Q3, Max (Correct answer)
- Min, mean, mode, Q3, Max
- Q1, Q2, Q3, IQR, Range
Correct answer: Min, Q1, Median, Q3, Max
A box plot is built from the five-number summary: minimum, Q1, median, Q3, and maximum.
DSST Statistics 4
A fair coin is flipped 10 times.
The probability of exactly 3 heads follows which distribution?