Which of the following sampling techniques is most likely to introduce bias?
Systematic sampling
Convenience sampling
Stratified random sampling
Simple random sampling
When would you use a paired t-test instead of an independent t-test?
When comparing the means of two groups with unequal variances.
When comparing the means of the same group before and after a treatment.
When comparing the means of two independent groups.
When comparing the means of three or more groups.
When is Spearman's rank correlation a more appropriate measure of association than Pearson's correlation?
When the relationship between variables is perfectly linear
When outliers are not present in the data
When the relationship between variables is non-linear but monotonic
When the variables are measured on an interval or ratio scale and normally distributed
What pattern in residual analysis might suggest that a linear model is not appropriate for the data?
Randomly scattered residuals
All residuals clustered around zero
A curved pattern in the residuals
Residuals consistently increasing with increasing values of the independent variable
What is the range of possible values for the coefficient of determination (R²)?
Depends on the data
-∞ to +∞
-1 to 1
0 to 1
In factor analysis, what does the term 'communality' refer to?
The uniqueness of a particular variable
The proportion of variance in a variable explained by all factors
The correlation between two factors
The eigenvalue of a factor
Which of the following is NOT a key assumption of the Central Limit Theorem?
The population has a finite mean and variance.
The samples are independent and randomly selected.
The population distribution is normal.
The sample size is sufficiently large (generally n ≥ 30).
An autoregressive model (AR) uses ______ values of the time series to predict future values.
Past
Average
Future
Random
In ANOVA, what does the F-statistic represent?
The difference between the smallest and largest group means.
The correlation coefficient between the independent and dependent variables.
The probability of observing the data if all group means were equal.
The ratio of between-group variance to within-group variance.
A normal distribution has a mean of 50 and a standard deviation of 10. What is the probability that a randomly selected value from this distribution is between 40 and 60?
0.9973
0.3413
0.9545
0.6827