4. Probability

Suppose you are given the following data for two variables, $X$ and $Y$: $(1,2)$, $(2,4)$, $(3,6)$, $(4,8)$. What is the value of the sample correlation coefficient between $X$ and $Y$? Do not round your intermediate calculations.

Suppose a researcher wants to determine the average height of all students currently enrolled at a large university. Should the researcher collect data from a sample or from the entire population?

Given any two events $A$ and $B$, which of the following correctly expresses the probability of their union $P(A\cup B)$?

Given a table that lists the number of cars sold by a dealership each day, is the random variable representing the number of cars sold discrete or continuous?

Which of the following best describes the difference between a $\mathrm{census}$ and a $\mathrm{sampling}$ in statistics?

Suppose a standard deck contains cards that are either striped or solid, and either blue or red. If the probability that a card is striped is $\frac{1}{2}$ and the probability that a card is blue is $\frac{1}{4}$, and being striped and being blue are independent events, what is the probability that a randomly selected card is both striped and blue?

A racehorse wins $5$ of its first $7$ races. What is the ratio of the number of races won to the number of races lost?

Which two essential features are present in all statistically designed experiments?

In the context of probability, what does it mean when sampling is done without replacement?

A simple random sample from an infinite population is a sample selected such that:

In the context of basic probability, does a $probability$ distribution function always have to be defined by a mathematical formula with parameters?

Which of the following is an advantage of using surveys for data collection in probability studies?

Are data at the $\mathrm{nominal}$ level of measurement considered $\mathrm{quantitative}$ or $\mathrm{qualitative}$?

In the context of probability, which of the following best describes a $\mathrm{marginal}$ distribution as compared to a $\mathrm{conditional}$ distribution?