A Chi-square test is used to:
Analyze the variance within and between groups.
Analyze the relationship between two categorical variables.
Determine if a sample mean is significantly different from a known population mean.
Compare the means of two groups.
In exponential smoothing, a higher value of the smoothing parameter (alpha) gives _______ weight to recent observations.
Lower
Higher
Zero
Equal
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 data is categorical.
The observations are independent.
The lifetime of a certain electronic component follows an exponential distribution with a mean of 10,000 hours. What is the probability that a randomly selected component lasts less than 5,000 hours?
0.5
0.25
0.6321
0.3935
A random variable follows a uniform distribution between 0 and 10. What is the probability that the variable takes a value between 3 and 7?
0.7
0.4
0.3
Which of the following is an example of a non-parametric inferential statistical test?
Chi-square test
z-test
t-test
ANOVA
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?
$0.00
$2.50
$5.00
-$2.50
What does a residual in regression analysis represent?
The intercept of the regression line
The difference between the observed value and the predicted value of the dependent variable
The correlation between the independent and dependent variables
The slope of the regression line
What is the null hypothesis in a Chi-square test of independence?
The two variables are dependent.
The means of the two groups are equal.
The two variables are independent.
The variances of the two groups are equal.
In PCA, what does a scree plot help determine?
The correlation between principal components
The amount of variance explained by each variable
The optimal number of principal components to retain
The presence of multicollinearity