What is the measure of central tendency that divides a data set into two equal halves?
- Mean
- Median
- Mode
- Range
The median is the measure of central tendency that divides a data set into two equal halves. When the observations are ordered from smallest to largest, the median is the middle value, ensuring that 50% of the data falls below and 50% above the median value.
The larger the number of observations, the closer the sample mean will be to the population mean, according to the _________.
- Central Limit Theorem
- Law of Large Numbers
- Probability Rule
- Sampling Distribution
According to the Law of Large Numbers, the larger the number of observations, the closer the sample mean will be to the population mean. This law is a fundamental principle of probability and statistics that states that as the size of a sample is increased, the estimate of certain parameters obtained from the sample will tend to approach the true value for the population.
What happens if the Kruskal-Wallis Test results in a statistically significant H value?
- It means nothing
- It means the groups are different
- It means the groups are the same
- It means the test failed
A statistically significant H value in the Kruskal-Wallis Test suggests that at least one of the sample distributions is different from the others.
How is the Chi-square distribution related to the normal distribution?
- The Chi-square distribution is a special case of the normal distribution
- The Chi-square distribution is the distribution of the square of a standard normal random variable
- The Chi-square distribution is the distribution of the sum of two standard normal random variables
- The normal distribution is a special case of the Chi-square distribution
The Chi-square distribution is related to the normal distribution in that it is the distribution of the square of a standard normal random variable.
Quantitative data can be broken down into two types: ________ and ________.
- Continuous, Categorical
- Discrete, Continuous
- Nominal, Ordinal
- Ratio, Interval
Quantitative data can be broken down into two types: Discrete and Continuous. Discrete data can only take specific values (like whole numbers) while Continuous data can take any value (within a range).
How many groups or variables does a two-way ANOVA test involve?
- 1
- 2
- 3 or more
- Not restricted
A two-way ANOVA involves two independent variables, each with any number of levels/groups. It allows simultaneous analysis of the effects of these variables.
What is the purpose of a Chi-square test for independence?
- To compare the means of two groups
- To compare the variance of two groups
- To test for a relationship between two categorical variables
- To test the difference between an observed distribution and a theoretical distribution
The Chi-square test for independence is used to test for a relationship or association between two categorical variables.
If events A and B are independent, then the probability of both events is the product of their individual probabilities, i.e., P(A ∩ B) = _______.
- P(A) * P(B)
- P(A) + P(B)
- P(A) - P(B)
- P(A) / P(B)
If events A and B are independent, the probability of both events occurring is the product of their individual probabilities, i.e., P(A ∩ B) = P(A) * P(B). This is a direct consequence of the Multiplication Rule for independent events.
Why is the Central Limit Theorem important in statistics?
- It provides the basis for linear regression.
- It simplifies the analysis of data and allows for easier predictions.
- It's not important; it's just a theory.
- It's only used in quantum physics.
The Central Limit Theorem (CLT) is important in statistics because it allows statisticians to make inferences about the population mean and standard deviation based on the properties of the sample mean. It simplifies many aspects of statistical inference by allowing us to make approximate calculations that are sufficiently accurate for large sample sizes.
What are the implications of a negative Pearson's Correlation Coefficient?
- The variables are inversely related
- There is a strong negative relationship
- There is a strong positive relationship
- There is no relationship
A negative Pearson's Correlation Coefficient means the variables are inversely related. As one variable increases, the other tends to decrease, and vice versa. The closer the coefficient is to -1, the stronger this inverse or negative relationship is.