Question 1

Which of the following best describes the purpose of inferential statistics?

Accepted Answer

To make predictions or inferences about a population based on a sample.

Question 2

A researcher collects data on the heights of 100 randomly selected college students. Which of the following is the sample in this scenario?

Accepted Answer

The 100 randomly selected college students.

Question 3

Which formula correctly represents the calculation of the sample mean $$\bar{x}$$ for a dataset with $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{\sum_{i=1}^n x_i}{n}$$

Question 4

Which of the following is NOT a measure of central tendency?

Accepted Answer

Variance

Question 5

A pharmaceutical company wants to test if a new drug lowers blood pressure more effectively than the current standard. Which statistical method should they use?

Accepted Answer

Hypothesis testing

Question 6

Which of the following formulas is used to calculate the sample variance $$s^2$$?

Accepted Answer

$$s^2$$ = \frac{\sum_{i=1}^n (x_i - \bar{x}$$)^2$$}{n-1}$$

Question 7

If the probability of rain tomorrow is 0.3, what is the probability that it will NOT rain?

Accepted Answer

$$0.7$$

Question 8

Which of the following statements about the normal distribution is TRUE?

Accepted Answer

It is symmetric about the mean.

Question 9

A hospital administrator wants to estimate the average waiting time in the emergency room. Which of the following best describes the population parameter of interest?

Accepted Answer

The average waiting time of all patients in the emergency room.

Question 10

Which of the following is an example of a discrete random variable?

Accepted Answer

The number of cars passing through an intersection in an hour.

Question 11

Suppose the probability of a defective item from a factory is 0.02. If 5 items are selected at random, what is the expected number of defective items?

Accepted Answer

$$0.1$$

Question 12

Which of the following best describes the law of large numbers?

Accepted Answer

As the sample size increases, the sample mean approaches the population mean.

Question 13

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$ and $$A$$ and $$B$$ are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.2$$

Question 14

Which of the following is a property of the standard deviation?

Accepted Answer

It is always non-negative.

Question 15

A researcher wants to test if a coin is fair. Which hypothesis test should be used?

Accepted Answer

A test for proportions

Probability and Random Variables: Foundational Concepts in Statistics

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