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What does it mean that a variable is measured at the ratio scale of measurement?
Equal intervals: Differences between values are consistent.
Absolute zero: A true zero point exists,
meaning “none” of the quantity is present.
Ratios are meaningful: For example, 20 is twice as much as 10.
Give an example of a variable measured at the ratio scale.
Height (e.g., in cm or inches): Equal intervals, absolute zero, and meaningful ratios (200 cm is twice as tall as 100 cm).
Weight (e.g., in kg or lbs): A weight of 0 means no weight, and 10 kg is twice as heavy as 5 kg.
What is the difference between independent and mutually exclusive events?
Independent Events: The outcome of one does not affect the other; both can happen together.
Mutually Exclusive Events: The events cannot happen at the same time.
Give an example of two independent events.
Rolling a 6 on a dice and flipping a coin to get heads.
These events are independent because the outcome of one does not affect the other.
What is the Central Limit Theorem (CLT)?
If you take many random samples and calculate their averages, the results will form a bell curve (normal distribution), even if the original data isn’t.
Sample averages will be close to the population’s true average.
Larger samples give more accurate results
Give an example of when the Central Limit Theorem is useful
Context: A teacher wants to know the average score of all students in a school.
How CLT Helps:
The teacher can test small random groups, calculate their averages, and use those to estimate the school-wide average.
Even if individual scores are uneven, the group averages will form a normal pattern.
Why should ANOVA not be replaced by repeated two-sample t-tests?
Increased Type I error: Multiple t-tests raise the risk of false positives.
Efficiency: ANOVA compares all groups in one test.
Broader insights: ANOVA checks if any group differs, while t-tests only compare pairs.
What are the assumptions of ANOVA?
Independence: Observations in each group are independent.
Normality: Data in each group follows a normal distribution.
Homogeneity of variance: Variances within groups are roughly the same.
What is a population?
A population is the entire group of individuals or items that a researcher wants to study or gather information about. It includes all possible subjects that fit a specific set of criteria.
Provide an example of a population, ensuring the context is presented.
Context: A school principal wants to understand student satisfaction with cafeteria food.
Population: All students enrolled in the school, as they are the group the principal is interested in studying.
In hypothesis testing, what is meant by matched sample design?
A matched sample design involves pairing subjects based on similarities (e.g., age, gender, or other characteristics).
One member of each pair is randomly assigned to the treatment group, and the other to the control group.
This design helps control for confounding variables by ensuring comparisons are between similar subjects.
Provide an example of when a matched sample design is used, ensuring the context is presented.
A researcher wants to test the effect of a new teaching method on student performance.
Example: Students are paired based on their initial test scores, and one student in each pair is assigned to the new teaching method while the other is assigned to the traditional method. This controls for initial differences in ability.
How can one make the confidence interval smaller?
Increase the sample size: A larger sample provides more precise estimates, narrowing the confidence interval.
Decrease the confidence level: Reducing the confidence level (e.g., from 99% to 95%) results in a smaller interval, but with less certainty.
What is the difference between combinations and permutations?
Combinations: The order of selection does not matter. It is used when selecting items without regard to the arrangement.
Permutations: The order of selection does matter. It is used when the arrangement of items is important.
Q: Give an example of when you would use the concept of combinations.
Context: You are selecting 3 players from a group of 10 for a team.
Example: The order of selecting the players doesn’t matter, so you would use combinations to calculate the number of ways to choose 3 players from 10.
