MRA Statistical Techniques & Data Interpretation 2 — Questions and Answers
Question 1: A researcher conducts an ANOVA test and obtains a p-value of 0.03 with an alpha of 0.05. What is the correct conclusion?
- Fail to reject the null hypothesis
- Reject the null hypothesis; at least one group mean differs (Correct answer)
- All group means are equal
- The test is inconclusive
Correct answer: Reject the null hypothesis; at least one group mean differs
Because p (0.03) < alpha (0.05), we reject the null hypothesis and conclude at least one group mean is significantly different.
Question 2: In regression analysis, what does a coefficient of determination (R²) of 0.85 indicate?
- 85% of the variance in the dependent variable is explained by the model (Correct answer)
- The slope of the regression line is 0.85
- There is an 85% chance the model is correct
- 85% of data points fall on the regression line
Correct answer: 85% of the variance in the dependent variable is explained by the model
R² represents the proportion of variance in the outcome variable that is explained by the predictor(s) in the model.
Question 3: Which measure of central tendency is most appropriate when data contains extreme outliers?
- Mean
- Median (Correct answer)
- Mode
- Weighted average
Correct answer: Median
The median is resistant to outliers because it reflects the middle value rather than the arithmetic average of all values.
Question 4: A market researcher uses a chi-square test on survey data. What type of data is this test designed for?
- Continuous interval data
- Ordinal ranked data
- Categorical (nominal) data (Correct answer)
- Ratio-scale data only
Correct answer: Categorical (nominal) data
The chi-square test of independence is used to evaluate relationships between categorical (nominal) variables using frequency counts.
Question 5: When a confidence interval for a mean is reported as (42, 58), what does this mean?
- The true mean is definitely between 42 and 58
- We are confident (at the stated level) that the interval captures the true population mean (Correct answer)
- 42 and 58 are the minimum and maximum sample values
- There is a 5% chance the mean equals 50
Correct answer: We are confident (at the stated level) that the interval captures the true population mean
A confidence interval means that if we repeated the study many times, the stated percentage of such intervals would contain the true parameter.
Question 6: What is multicollinearity in a multiple regression model?
- When the dependent variable has multiple modes
- When two or more predictor variables are highly correlated with each other (Correct answer)
- When residuals are not normally distributed
- When the sample size is too small for the number of predictors
Correct answer: When two or more predictor variables are highly correlated with each other
Multicollinearity occurs when independent variables are strongly correlated, making it difficult to isolate each predictor's individual effect on the outcome.
Question 7: A researcher reports a Cronbach's alpha of 0.91 for a 10-item scale. What does this indicate?
- The scale has poor internal consistency
- 90.1% of items were answered correctly
- The scale has excellent internal consistency (Correct answer)
- Only 9 of the 10 items are valid
Correct answer: The scale has excellent internal consistency
Cronbach's alpha above 0.90 generally indicates excellent internal consistency, meaning the items reliably measure the same underlying construct.
MRA Statistical Techniques & Data Interpretation 2
A researcher conducts an ANOVA test and obtains a p-value of 0.03 with an alpha of 0.05.
What is the correct conclusion?