In factor analysis, what does the term 'communality' refer to?
The eigenvalue of a factor
The proportion of variance in a variable explained by all factors
The uniqueness of a particular variable
The correlation between two factors
A Chi-square test is most appropriate for analyzing which type of data?
Time series data
Continuous data
Normally distributed data
Categorical data
Which of the following smoothing methods is most appropriate when the time series data exhibits a trend but no seasonality?
Moving Average Smoothing
Triple Exponential Smoothing
Simple Exponential Smoothing
Double Exponential Smoothing
A 95% confidence interval for a population mean is calculated to be (60, 80). What is the correct interpretation of this interval?
If we were to repeatedly construct confidence intervals using this method, 95% of them would contain the true population mean.
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.
We are 95% confident that the sample mean falls between 60 and 80.
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?
0.05
0.996
0.57
0.004
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
$0.00
-$2.50
$2.50
If the variance of a random variable is 9, what is its standard deviation?
3
81
9
18
What does a Pearson correlation coefficient of -0.9 suggest about the relationship between two variables?
No linear relationship
Strong negative linear relationship
Strong positive linear relationship
Weak positive linear relationship
What is the null hypothesis in a Chi-square test of independence?
The two variables are dependent.
The two variables are independent.
The means of the two groups are equal.
The variances of the two groups are equal.
What is the primary goal of factor rotation in factor analysis?
To improve the interpretability of factors
To increase the communalities of variables
To calculate the eigenvalues of factors
To reduce the number of factors