Which of the following statements is TRUE about multivariate analysis of variance (MANOVA)?
It examines the relationship between two continuous variables.
It analyzes the differences between groups on multiple dependent variables simultaneously.
It is used for dimensionality reduction of categorical variables.
It tests the difference in means between two groups on a single dependent variable.
In simple linear regression, what does a negative slope of the regression line indicate?
As the independent variable increases, the dependent variable increases.
There is no relationship between the independent and dependent variables.
As the independent variable increases, the dependent variable decreases.
The relationship between the independent and dependent variables is non-linear.
Principal Component Analysis (PCA) is primarily a ______ technique.
Regression
Dimensionality Reduction
Clustering
Classification
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?
0.6321
0.5
0.3935
0.25
What is the primary difference between simple exponential smoothing and double exponential smoothing?
Simple exponential smoothing uses a moving average, while double exponential smoothing uses an autoregressive model.
Double exponential smoothing is used for stationary data, while simple exponential smoothing is used for non-stationary data.
Simple exponential smoothing considers seasonality, while double exponential smoothing does not.
Double exponential smoothing considers trend, while simple exponential smoothing does not.
A 95% confidence interval for a population mean is calculated to be (60, 80). What is the correct interpretation of this interval?
We are 95% confident that the sample mean falls between 60 and 80.
There is a 95% probability that the true population mean falls between 60 and 80.
If we were to repeatedly sample from this population, 95% of the time the sample mean would fall between 60 and 80.
If we were to repeatedly construct confidence intervals using this method, 95% of them would contain the true population mean.
As the sample size increases, the standard error of the mean:
Cannot be determined
Decreases
Increases
Stays the same
A Chi-square test is most appropriate for analyzing which type of data?
Categorical data
Normally distributed data
Time series data
Continuous data
Let X be a random variable representing the number of heads when you toss a fair coin three times. What is the variance of X?
0.75
1.5
1
If the variance of a random variable is 9, what is its standard deviation?
18
3
81
9