Which of the following is NOT an assumption of a two-sample t-test?
The two groups are dependent on each other.
The data in each group are normally distributed.
The data points within each group are independent.
The variances of the two groups are equal.
What is the range of possible values for the coefficient of determination (R²)?
Depends on the data
-∞ to +∞
0 to 1
-1 to 1
What is the purpose of using a correlation matrix in multivariate statistics?
To assess the strength and direction of linear relationships between pairs of variables
To visualize the distribution of residuals in regression
To determine the optimal number of factors in factor analysis
To identify outliers in a dataset
The sampling distribution of a statistic is:
The distribution of the statistic in a single random sample.
Always normally distributed.
The distribution of the statistic across all possible samples of a given size.
The same as the population distribution.
In multiple regression, what does a high variance inflation factor (VIF) indicate?
Low multicollinearity among predictor variables
High multicollinearity among predictor variables
Heteroscedasticity in the residuals
A good fit of the regression model
Which of the following is NOT an assumption of a t-test?
The data is normally distributed.
The variances of the groups being compared are equal (for independent samples t-test).
The observations are independent.
The data is categorical.
As the sample size increases, the standard error of the mean:
Cannot be determined
Stays the same
Decreases
Increases
A company manufactures light bulbs. The probability that a bulb is defective is 0.05. If you choose 3 bulbs at random, what is the probability that at least one bulb is defective?
0.143
0.999875
0.000125
0.857
You want to compare the average heights of men and women in a population. Which hypothesis test would be most appropriate?
One-sample t-test
Paired t-test
Independent samples t-test
Chi-square test
What is the null hypothesis in a Chi-square test of independence?
The two variables are independent.
The two variables are dependent.
The means of the two groups are equal.