MRA Statistical Analysis & Interpretation 2 — Questions and Answers
Question 1: A researcher finds a correlation of r = 0.85 between advertising spend and sales. What percentage of the variance in sales is explained by advertising spend?
- 85%
- 72.25% (Correct answer)
- 92.2%
- 0.85%
Correct answer: 72.25%
R-squared = r² = 0.85² = 0.7225, so 72.25% of variance is explained.
Question 2: When conducting a two-sample t-test, what assumption must be verified about the populations?
- They must have equal sample sizes
- They must be normally distributed or have large enough samples (Correct answer)
- They must have identical means
- They must be collected simultaneously
Correct answer: They must be normally distributed or have large enough samples
The two-sample t-test assumes normality of populations or relies on the Central Limit Theorem with sufficiently large samples.
Question 3: A market researcher uses a Likert scale from 1-5. What is the most appropriate measure of central tendency to report?
- Mean
- Median (Correct answer)
- Mode
- Range
Correct answer: Median
Median is preferred for ordinal Likert data because it respects rank order without assuming equal intervals.
Question 4: In ANOVA, the F-statistic is calculated as the ratio of which two quantities?
- Between-group variance to within-group variance (Correct answer)
- Within-group variance to between-group variance
- Sample mean to population mean
- Standard deviation to standard error
Correct answer: Between-group variance to within-group variance
F = Mean Square Between / Mean Square Within; a high F indicates group means differ more than expected by chance.
Question 5: A study reports p = 0.03 with α = 0.05. Which conclusion is correct?
- Fail to reject the null hypothesis
- Reject the null hypothesis (Correct answer)
- The effect size is large
- The result is practically significant
Correct answer: Reject the null hypothesis
Since p (0.03) < α (0.05), the result is statistically significant and the null hypothesis is rejected.
Question 6: What does a box plot's interquartile range (IQR) represent?
- The distance between the minimum and maximum
- The spread of the middle 50% of data (Correct answer)
- The distance between the mean and median
- The standard deviation of the data
Correct answer: The spread of the middle 50% of data
IQR = Q3 − Q1, capturing the range of the middle 50% of observations and indicating data spread.
Question 7: Which statistical test is most appropriate for comparing proportions across three or more independent groups?
- Independent samples t-test
- Paired t-test
- Chi-square test of independence (Correct answer)
- Pearson correlation
Correct answer: Chi-square test of independence
The chi-square test of independence evaluates whether categorical distributions differ significantly across multiple groups.
MRA Statistical Analysis & Interpretation 2
A researcher finds a correlation of r = 0.85 between advertising spend and sales.
What percentage of the variance in sales is explained by advertising spend?