What is the range of possible values for the coefficient of determination (R²)?
-∞ to +∞
-1 to 1
Depends on the data
0 to 1
A random variable X has the following probability distribution: P(X=0) = 0.2, P(X=1) = 0.3, P(X=2) = 0.5. What is the expected value of X?
1
1.2
0.5
1.5
The number of cars passing a certain point on a highway averages 10 per hour. What is the probability that exactly 15 cars pass that point in a given hour?
0.15
0.25
0.0347
What is a Type II error in hypothesis testing?
Incorrectly calculating the p-value.
Using the wrong test statistic for the data.
Rejecting the null hypothesis when it is true.
Failing to reject the null hypothesis when it is false.
Principal Component Analysis (PCA) is primarily a ______ technique.
Classification
Regression
Dimensionality Reduction
Clustering
Which of the following is NOT an assumption of a t-test?
The data is normally distributed.
The data is categorical.
The observations are independent.
The variances of the groups being compared are equal (for independent samples t-test).
Suppose 60% of emails in your inbox are spam and 40% are legitimate. Also, 95% of spam emails contain the word 'free,' while only 1% of legitimate emails do. If an email contains the word 'free,' what's the probability it's spam?
0.004
0.05
0.996
0.57
Which of the following is NOT an assumption of a two-sample t-test?
The two groups are dependent on each other.
The variances of the two groups are equal.
The data points within each group are independent.
The data in each group are normally distributed.
What is the purpose of calculating a correlation coefficient?
To measure the strength and direction of the linear relationship between two variables.
To determine the cause-and-effect relationship between two variables.
To test the significance of the difference between two means.
To predict the value of one variable based on the value of another variable.
When is ANOVA (Analysis of Variance) used instead of a t-test?
When comparing the variances of two groups.
When analyzing the relationship between two categorical variables.
When comparing the means of three or more groups.
When comparing the means of two groups.