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).
What is the key difference between a t-test and an ANOVA?
- t-test is for one variable, ANOVA is for two variables
- t-test is for three groups, ANOVA is for two groups
- t-test is for two groups, ANOVA is for three or more groups
- t-test is for two variables, ANOVA is for one variable
The key difference between a t-test and an ANOVA is the number of groups being compared. A t-test is used to compare the means of two groups, while ANOVA is used to compare the means of three or more groups.
What does inferential statistics allow you to do?
- Collect data
- Describe data
- Organize data
- Predict or make inferences about a population
Inferential statistics is a branch of statistics that allows us to use data from a sample to infer or predict trends about the overall population. This technique is immensely useful as it's often impractical or impossible to collect data from an entire population. Inferential statistics makes use of various techniques such as probability, hypothesis testing, correlation, and regression to draw conclusions.
How does Bayes' theorem assist in decision making under uncertainty?
- It eliminates all uncertainty
- It proves the correctness of an assumption
- It provides a method for incorporating new data to update our beliefs
- It reduces the data needed for decision making
Bayes' Theorem provides a mathematical framework for updating probabilities, which can be interpreted as degrees of belief, based on the evidence at hand. Thus, it assists in decision making under uncertainty by allowing for the incorporation of new information.
How does the Kruskal-Wallis Test handle ties between ranks?
- Assigns them average ranks
- Discards them
- Ignores them
- Treats them as errors
When two or more data points have the same value, they are considered tied. The Kruskal-Wallis Test assigns them the average of the ranks that the tied values would have received had they been different.
Why might the confidence interval for a proportion be skewed?
- Because of a large sample size
- Because of a small sample size
- Because the proportion is around 0.5
- Because the proportion is close to 0 or 1
A confidence interval for a proportion might be skewed when the proportion is very close to 0 or 1. In these cases, the distribution of sample proportions is not symmetrical, leading to skewed intervals.
A negative Spearman's rank correlation coefficient indicates a(n) ________ association between two variables.
- Direct
- Inverse
- Positive
- Strong
A negative Spearman's rank correlation coefficient indicates an inverse association between two variables. That is, as one variable increases, the other tends to decrease.