Statistics Final Examination Questions and Answers
with Verified Solutions
Comprehensive Examination Review & Master Solution Key
1. Which measure of central tendency is most sensitive to extreme outliers in a skewed
continuous dataset?
A. Median
B. Mode
C. Mean
D. Interquartile Range
Rationale: The arithmetic mean incorporates every numerical observation in its calculation,
making it highly sensitive to extreme values or outliers compared to robust measures like
the median or mode.
2. A researcher calculates a p-value of 0.025 for a hypothesis test using an alpha level (α) of 0.05.
What is the correct statistical decision?
A. Reject the null hypothesis
B. Fail to reject the null hypothesis
C. Accept the null hypothesis as true
D. Increase the sample size and retest
Rationale: When the calculated p-value is less than or equal to the significance level (α =
0.05), there is sufficient statistical evidence to reject the null hypothesis.
3. What statistical error occurs when a researcher rejects a true null hypothesis?
A. Type I Error
B. Type II Error
C. Measurement Error
D. Sampling Error
Rationale: A Type I error (α) occurs when a researcher incorrectly rejects a null hypothesis
that is actually true (a false positive result).
4. Which measure of variability represents the average squared deviation of data points from the
sample mean?
, A. Standard Deviation
B. Variance
C. Range
D. Mean Absolute Deviation
Rationale: Variance measures the dispersion of continuous data points by taking the
average of their squared distances from the mean. Standard deviation is the square root of
variance.
5. According to the Central Limit Theorem, as sample size (n) increases, what shape does the
sampling distribution of the sample mean approach?
A. Uniform distribution
B. Bimodal distribution
C. Normal distribution
D. Positively skewed distribution
Rationale: The Central Limit Theorem states that as sample size increases
(typically n ≥ 30), the sampling distribution of the sample mean approaches a
normal distribution regardless of the population distribution shape.
6. What statistical test is used to compare the means of three or more independent groups?
A. Independent samples t-test
B. Paired samples t-test
C. One-Way Analysis of Variance (ANOVA)
D. Chi-square test of independence
Rationale: One-Way ANOVA evaluates whether significant mean differences exist across
three or more categorical treatment groups while controlling for inflation of Type I error
rates.
7. A Pearson correlation coefficient (r) of -0.85 indicates what relationship between two
continuous variables?
A. Weak negative linear relationship
B. Strong negative linear relationship
C. Strong positive linear relationship
D. No linear relationship
Rationale: Pearson's r ranges from -1.00 to +1.00. An r-value close to -1.0 (such as -0.85)
signifies a strong inverse linear association where one variable increases as the other
decreases.
with Verified Solutions
Comprehensive Examination Review & Master Solution Key
1. Which measure of central tendency is most sensitive to extreme outliers in a skewed
continuous dataset?
A. Median
B. Mode
C. Mean
D. Interquartile Range
Rationale: The arithmetic mean incorporates every numerical observation in its calculation,
making it highly sensitive to extreme values or outliers compared to robust measures like
the median or mode.
2. A researcher calculates a p-value of 0.025 for a hypothesis test using an alpha level (α) of 0.05.
What is the correct statistical decision?
A. Reject the null hypothesis
B. Fail to reject the null hypothesis
C. Accept the null hypothesis as true
D. Increase the sample size and retest
Rationale: When the calculated p-value is less than or equal to the significance level (α =
0.05), there is sufficient statistical evidence to reject the null hypothesis.
3. What statistical error occurs when a researcher rejects a true null hypothesis?
A. Type I Error
B. Type II Error
C. Measurement Error
D. Sampling Error
Rationale: A Type I error (α) occurs when a researcher incorrectly rejects a null hypothesis
that is actually true (a false positive result).
4. Which measure of variability represents the average squared deviation of data points from the
sample mean?
, A. Standard Deviation
B. Variance
C. Range
D. Mean Absolute Deviation
Rationale: Variance measures the dispersion of continuous data points by taking the
average of their squared distances from the mean. Standard deviation is the square root of
variance.
5. According to the Central Limit Theorem, as sample size (n) increases, what shape does the
sampling distribution of the sample mean approach?
A. Uniform distribution
B. Bimodal distribution
C. Normal distribution
D. Positively skewed distribution
Rationale: The Central Limit Theorem states that as sample size increases
(typically n ≥ 30), the sampling distribution of the sample mean approaches a
normal distribution regardless of the population distribution shape.
6. What statistical test is used to compare the means of three or more independent groups?
A. Independent samples t-test
B. Paired samples t-test
C. One-Way Analysis of Variance (ANOVA)
D. Chi-square test of independence
Rationale: One-Way ANOVA evaluates whether significant mean differences exist across
three or more categorical treatment groups while controlling for inflation of Type I error
rates.
7. A Pearson correlation coefficient (r) of -0.85 indicates what relationship between two
continuous variables?
A. Weak negative linear relationship
B. Strong negative linear relationship
C. Strong positive linear relationship
D. No linear relationship
Rationale: Pearson's r ranges from -1.00 to +1.00. An r-value close to -1.0 (such as -0.85)
signifies a strong inverse linear association where one variable increases as the other
decreases.
