When is ANOVA (Analysis of Variance) used instead of a t-test?
When analyzing the relationship between two categorical variables.
When comparing the variances of two groups.
When comparing the means of three or more groups.
When comparing the means of two groups.
In exponential smoothing, a higher value of the smoothing parameter (alpha) gives _______ weight to recent observations.
Zero
Higher
Equal
Lower
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?
0.25
0.0347
0.15
0.5
An autoregressive model (AR) uses ______ values of the time series to predict future values.
Past
Future
Average
Random
In PCA, what does a scree plot help determine?
The presence of multicollinearity
The correlation between principal components
The amount of variance explained by each variable
The optimal number of principal components to retain
As the sample size increases, the standard error of the mean:
Increases
Decreases
Stays the same
Cannot be determined
In ANOVA, what does the F-statistic represent?
The probability of observing the data if all group means were equal.
The difference between the smallest and largest group means.
The correlation coefficient between the independent and dependent variables.
The ratio of between-group variance to within-group variance.
Which of the following is NOT an assumption of a t-test?
The observations are independent.
The variances of the groups being compared are equal (for independent samples t-test).
The data is normally distributed.
The data is categorical.
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?
1.5
1.2
1
You're playing a game where you flip a coin. Heads, you win $10. Tails, you lose $5. What is the expected value of playing this game?
$5.00
-$2.50
$2.50
$0.00