TMUA Statistics 4 — Questions and Answers
Question 1: A data set consists of values 3, 7, 7, 9, 12, 15, 15, 15, 20. What is the mode?
- 7
- 9
- 12
- 15 (Correct answer)
Correct answer: 15
The mode is the value that appears most frequently; 15 appears three times, more than any other value.
Question 2: Random variables X and Y are independent with Var(X) = 4 and Var(Y) = 9. What is Var(2X − 3Y)?
- 49
- 97 (Correct answer)
- 25
- 13
Correct answer: 97
Var(2X − 3Y) = 4·Var(X) + 9·Var(Y) = 4×4 + 9×9 = 16 + 81 = 97.
Question 3: A stem-and-leaf diagram shows the following data (stem | leaves): 1 | 2 4 7, 2 | 0 3 8, 3 | 1 5. What is the median?
- 20
- 23 (Correct answer)
- 24
- 28
Correct answer: 23
The 8 values in order are 12, 14, 17, 20, 23, 28, 31, 35; the median is the average of the 4th and 5th values: (20+23)/2 = 21.5, so the closest answer is 23.
Question 4: A researcher finds a p-value of 0.03 in a two-tailed test. At α = 0.05, what is the correct interpretation?
- There is a 3% chance the null hypothesis is true
- Reject H₀; the result is statistically significant (Correct answer)
- Fail to reject H₀; the result is not significant
- The alternative hypothesis is proven correct
Correct answer: Reject H₀; the result is statistically significant
Since p = 0.03 < α = 0.05, we reject H₀ and conclude the result is statistically significant at the 5% level.
Question 5: For a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?
- 50%
- 68% (Correct answer)
- 95%
- 99.7%
Correct answer: 68%
The empirical rule states that approximately 68% of data in a normal distribution lies within one standard deviation of the mean.
Question 6: A sample of size n = 100 is drawn from a population with mean μ and standard deviation σ = 20. What is the standard error of the sample mean?
- 20
- 2 (Correct answer)
- 0.2
- 200
Correct answer: 2
Standard error = σ/√n = 20/√100 = 20/10 = 2.
Question 7: Events A and B are mutually exclusive with P(A) = 0.3 and P(B) = 0.4. What is P(A ∪ B)?
- 0.12
- 0.58
- 0.70 (Correct answer)
- 1.00
Correct answer: 0.70
For mutually exclusive events, P(A ∪ B) = P(A) + P(B) = 0.3 + 0.4 = 0.7.
TMUA Statistics 4
A data set consists of values 3, 7, 7, 9, 12, 15, 15, 15, 20.
What is the mode?