DSST Statistics 5 — Questions and Answers
Question 1: In a simple linear regression equation ŷ = 3 + 2x, if x increases by 1, ŷ:
- Increases by 3
- Increases by 2 (Correct answer)
- Decreases by 2
- Stays the same
Correct answer: Increases by 2
The slope coefficient (2) indicates the change in ŷ for each one-unit increase in x.
Question 2: The Central Limit Theorem states that the sampling distribution of the sample mean approaches normality as:
- The population becomes normal
- The population variance decreases
- Sample size increases (Correct answer)
- The number of samples decreases
Correct answer: Sample size increases
As n increases (generally n ≥ 30), the distribution of sample means approximates a normal distribution regardless of the population shape.
Question 3: Which statistic is used to measure the spread of data around the regression line?
- Coefficient of variation
- Standard error of the estimate (Correct answer)
- Pearson's r
- Coefficient of determination
Correct answer: Standard error of the estimate
The standard error of the estimate (Sₑ) measures the average distance of observed values from the regression line.
Question 4: When two events are mutually exclusive, P(A or B) equals:
- P(A) × P(B)
- P(A) + P(B) - P(A and B)
- P(A) + P(B) (Correct answer)
- P(A) / P(B)
Correct answer: P(A) + P(B)
Mutually exclusive events cannot occur together, so P(A and B) = 0 and P(A or B) = P(A) + P(B).
Question 5: A researcher increases the alpha level from 0.01 to 0.05. This change:
- Decreases the probability of a Type I error
- Increases the probability of a Type I error (Correct answer)
- Increases the probability of a Type II error
- Has no effect on error probabilities
Correct answer: Increases the probability of a Type I error
Alpha is the Type I error rate; raising it from 0.01 to 0.05 increases the chance of incorrectly rejecting a true null.
Question 6: Which of the following is an example of a discrete random variable?
- The weight of a randomly chosen apple
- The time to complete a marathon
- The number of defects in a batch of 100 items (Correct answer)
- The temperature at noon tomorrow
Correct answer: The number of defects in a batch of 100 items
Count data (number of defects) can only take whole-number values, making it discrete.
Question 7: In a two-tailed hypothesis test with α = 0.05, each tail contains:
- 5% of the rejection region
- 2.5% of the rejection region (Correct answer)
- 10% of the rejection region
- 1% of the rejection region
Correct answer: 2.5% of the rejection region
For a two-tailed test, α is split equally between both tails, placing 0.025 (2.5%) in each.
DSST Statistics 5
In a simple linear regression equation ŷ = 3 + 2x, if x increases by 1, ŷ: