WGU C784 APPLIED PROBABILITY AND
STATISTICS ADVANCED
EXAMINATION 2026/2027
1. A researcher conducts a study and finds that the p-value is 0.02. If the predetermined
significance level is 0.05, what is the most appropriate conclusion?
A. Accept the null hypothesis as the result is statistically significant.
B. Reject the null hypothesis as the result is statistically significant.
C. Fail to reject the null hypothesis as the result is not significant.
D. The results are inconclusive because the p-value is greater than 0.01.
Answer: B
Conceptual Explanation: If the p-value is less than or equal to the significance level
(alpha), the result is considered statistically significant, and the null hypothesis is rejected.
2. Which of the following measurements is considered a ratio level of data?
A. Temperature in degrees Celsius
B. Political party affiliation
C. Annual income in dollars
D. Ranking of a race (1st, 2nd, 3rd)
,Answer: C
Conceptual Explanation: Ratio data has a true zero point, meaning that a value of zero
represents the absence of the characteristic. Annual income meets this criterion, unlike
Celsius temperature (interval) or rankings (ordinal).
3. In a negatively skewed distribution, which of the following relationships between the
mean, median, and mode is typically true?
A. Mean > Median > Mode
B. Mean = Median = Mode
C. Mean < Median < Mode
D. Median < Mean < Mode
Answer: C
Conceptual Explanation: In a negatively skewed distribution, the tail extends toward the
lower values, pulling the mean down the most, followed by the median, while the mode
remains at the peak.
4. A standard normal distribution has a mean of 0 and a standard deviation of 1. What
percentage of data falls between z = -2 and z = 2 according to the Empirical Rule?
A. 68%
B. 99.7%
C. 95%
, D. 50%
Answer: C
Conceptual Explanation: The Empirical Rule states that approximately 95% of the data
falls within two standard deviations (z = +/- 2) of the mean in a normal distribution.
5. If the correlation coefficient (r) between two variables is -0.85, how should the relationship
be described?
A. Strong negative linear relationship
B. Weak negative linear relationship
C. Strong positive linear relationship
D. No linear relationship
Answer: A
Conceptual Explanation: A correlation coefficient of -0.85 indicates a strong relationship
because it is close to -1, and negative because the value is less than zero.
6. What is the probability of rolling a sum of 4 with two fair six-sided dice?
A. 1/12
B. 1/36
C. 4/36
D. 3/36
STATISTICS ADVANCED
EXAMINATION 2026/2027
1. A researcher conducts a study and finds that the p-value is 0.02. If the predetermined
significance level is 0.05, what is the most appropriate conclusion?
A. Accept the null hypothesis as the result is statistically significant.
B. Reject the null hypothesis as the result is statistically significant.
C. Fail to reject the null hypothesis as the result is not significant.
D. The results are inconclusive because the p-value is greater than 0.01.
Answer: B
Conceptual Explanation: If the p-value is less than or equal to the significance level
(alpha), the result is considered statistically significant, and the null hypothesis is rejected.
2. Which of the following measurements is considered a ratio level of data?
A. Temperature in degrees Celsius
B. Political party affiliation
C. Annual income in dollars
D. Ranking of a race (1st, 2nd, 3rd)
,Answer: C
Conceptual Explanation: Ratio data has a true zero point, meaning that a value of zero
represents the absence of the characteristic. Annual income meets this criterion, unlike
Celsius temperature (interval) or rankings (ordinal).
3. In a negatively skewed distribution, which of the following relationships between the
mean, median, and mode is typically true?
A. Mean > Median > Mode
B. Mean = Median = Mode
C. Mean < Median < Mode
D. Median < Mean < Mode
Answer: C
Conceptual Explanation: In a negatively skewed distribution, the tail extends toward the
lower values, pulling the mean down the most, followed by the median, while the mode
remains at the peak.
4. A standard normal distribution has a mean of 0 and a standard deviation of 1. What
percentage of data falls between z = -2 and z = 2 according to the Empirical Rule?
A. 68%
B. 99.7%
C. 95%
, D. 50%
Answer: C
Conceptual Explanation: The Empirical Rule states that approximately 95% of the data
falls within two standard deviations (z = +/- 2) of the mean in a normal distribution.
5. If the correlation coefficient (r) between two variables is -0.85, how should the relationship
be described?
A. Strong negative linear relationship
B. Weak negative linear relationship
C. Strong positive linear relationship
D. No linear relationship
Answer: A
Conceptual Explanation: A correlation coefficient of -0.85 indicates a strong relationship
because it is close to -1, and negative because the value is less than zero.
6. What is the probability of rolling a sum of 4 with two fair six-sided dice?
A. 1/12
B. 1/36
C. 4/36
D. 3/36
