The null hypothesis for the Kruskal-Wallis Test states that all ________ have the same distribution.
- factors
- groups
- pairs
- variables
The null hypothesis for the Kruskal-Wallis Test states that all groups have the same distribution. It tests whether samples originate from the same distribution.
How does the correlation coefficient change when you switch the X and Y variables?
- It changes sign
- It decreases
- It increases
- It remains the same
The correlation coefficient remains the same when you switch the X and Y variables. This is because correlation measures the strength and direction of a relationship between two variables, not the dependency of one on the other.
What is meant by the term "multicollinearity" in multiple linear regression?
- The dependent variables are correlated with each other
- The error terms are correlated with each other
- The independent variables are correlated with each other
- The residuals are correlated with each other
In multiple linear regression, multicollinearity refers to a situation in which two or more independent variables are highly linearly related. This can cause problems because it can affect the interpretability of the regression coefficients and can make the model unstable.
In factor analysis, the relationship between each variable and the underlying factor is called a _______.
- factor correlation
- factor covariance
- factor loading
- factor variance
In factor analysis, the relationship between each variable and the underlying factor is called a factor loading.
What is a sample in the context of statistics?
- A chart showing population data
- A small group of people from a population
- A statistical calculation
- A type of population
In statistics, a sample refers to a subset of the population that is selected for study. The purpose of sampling is to draw conclusions about the entire population based on observations made on the sample. Since studying an entire population is often not feasible due to constraints such as time, cost, and accessibility, we rely on samples to gain insights about the population. Sampling, if done correctly, can provide a good approximation of the population and help in making inferences.
The process of estimation is made more precise by decreasing the _______ of the confidence interval.
- Confidence level
- Sample size
- Standard error
- Width
The precision of the estimation process increases as the width of the confidence interval decreases. A smaller width implies that the range of values within which the population parameter lies is narrower.
When is it appropriate to use quantitative data over qualitative data?
- Never
- When both measuring and categorizing are required
- When categorizing or describing is required
- When measuring or counting is required
Quantitative data is appropriate to use when measuring or counting is required, or when the data can be numerically quantified. This data type allows for statistical analysis and can provide a more objective and precise understanding than qualitative data. For example, it's appropriate to use quantitative data when you want to know how many people visited a website, how much customers are willing to pay for a product, or how often a certain event occurs.
What kind of hypothesis is tested in the Sign Test?
- The means of two groups are equal
- The medians of two groups are equal
- The proportions of two groups are equal
- The variances of two groups are equal
The Sign Test tests the null hypothesis that the medians of two groups are equal.
PCA assumes that the data follows a _______ distribution.
- Poisson
- binomial
- normal
- uniform
PCA makes the assumption that the data follows a multivariate normal distribution. This means that all linear combinations of the original variables also follow a normal distribution.
How does the concept of conditional probability relate to the Multiplication Rule?
- Conditional probabilities are the inverse of the Multiplication Rule
- The Multiplication Rule calculates conditional probabilities
- The Multiplication Rule can be rewritten using conditional probabilities
- They are unrelated concepts
Conditional probability and the Multiplication Rule are interconnected. The Multiplication Rule can be rewritten using conditional probabilities. Specifically, the Multiplication Rule states that the probability of two events A and B occurring (P(A ∩ B)) equals the probability of A given B (P(A