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(2 points) A box contains 4 red balls, 5 blue balls, and 6 green balls. Two balls are drawn at random without replacement. What is the probability that both balls are blue?

(2 points) A researcher fits a regression model and finds that all the predicted y-values fall close to the actual values. What does this suggest?

(2 points) A scatter plot shows that as students’ study time increases, their test scores tend to increase as well. What does this indicate about the correlation coefficient (r)?

(2 points) What is the significance level (alpha) used for in hypothesis testing?

A university event committee is forming a panel of 4 student speakers from a pool of 10 applicants. How many different combinations of 4 speakers can be selected if order does not matter? If the 4 selected students will speak in a specific order (introduction, keynote, response, and closing), how many different arrangements are possible? Explain the difference between the two results and why order matters in one case but not the other.

(2 points) A researcher compares the average exam scores of students taught using three different teaching methods. Which statistical test should be used?

(2 points) Which measure is identified for summarizing a frequency spread of values into a single value that suggests a typical observation?

(2 points) A researcher is studying the effect of sleep duration on student test performance but doesn’t account for caffeine intake. In this case, what role does caffeine consumption play in the study?

The scores on a standardized test are normally distributed with a mean of 500 and a standard deviation of 100. 1.  A student scores 650 on the test. What is their z-score?2.  Another student has a z-score of -1.5. What is their actual test score?3.  Explain what the z-score tells you about a student’s performance relative to the rest of the group.  

(2 points) Which statement best describes what the operator `%%` do in R?