In exponential smoothing, a higher value of the smoothing parameter (alpha) gives _______ weight to recent observations.
Higher
Lower
Equal
Zero
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?
0.3413
0.6827
0.9973
0.9545
Principal Component Analysis (PCA) is primarily a ______ technique.
Classification
Dimensionality Reduction
Clustering
Regression
A researcher wants to determine if a new drug reduces blood pressure more effectively than a placebo. They measure the blood pressure of the same group of patients before and after taking the drug and placebo (in random order). What test should they use?
Independent samples t-test
Paired t-test
One-sample t-test
ANOVA
Which of the following smoothing methods is most appropriate when the time series data exhibits a trend but no seasonality?
Moving Average Smoothing
Simple Exponential Smoothing
Triple Exponential Smoothing
Double Exponential Smoothing
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
0.5
When is ANOVA (Analysis of Variance) used instead of a t-test?
When comparing the means of three or more groups.
When comparing the variances of two groups.
When comparing the means of two groups.
When analyzing the relationship between two categorical variables.
What is the null hypothesis in a Chi-square test of independence?
The variances of the two groups are equal.
The two variables are independent.
The two variables are dependent.
The means of the two groups are equal.
A Chi-square test is used to:
Determine if a sample mean is significantly different from a known population mean.
Analyze the relationship between two categorical variables.
Analyze the variance within and between groups.
Compare the means of two groups.
Which of the following sampling techniques is most likely to introduce bias?
Stratified random sampling
Simple random sampling
Systematic sampling
Convenience sampling