Question 1

Which of the following best describes the difference between a sample and a population in statistics?

Accepted Answer

A sample is a subset of the population, used to make inferences about the population.

Question 2

A researcher wants to compare the average test scores of two different teaching methods. Which type of statistics should they use?

Accepted Answer

Inferential statistics, because they want to draw conclusions about the effectiveness of the methods.

Question 3

Which of the following is NOT a correct use of the SOCS framework when describing the distribution of quantitative data?

Accepted Answer

Reporting the mean for center and the IQR for spread if the data is skewed.

Question 4

A bar chart is used to display which type of data?

Accepted Answer

Categorical data only

Question 5

Suppose you are given a two-way table showing the relationship between smoking status (smoker/non-smoker) and lung disease (yes/no). To determine if there is an association, you should:

Accepted Answer

Compare the conditional proportions within each category of the explanatory variable.

Question 6

Which of the following statements about correlation is TRUE?

Accepted Answer

A correlation coefficient of $$r = -0.85$$ indicates a strong negative linear relationship.

Question 7

If events A and B are mutually exclusive, what is $$P(A \cap B)$$?

Accepted Answer

$$0$$

Question 8

A medical test for a rare disease has a 99% accuracy rate. If the disease occurs in 1 out of 10,000 people, what statistical concept is most relevant when interpreting a positive test result?

Accepted Answer

Conditional probability

Question 9

Which formula correctly represents the general addition rule for any two events A and B?

Accepted Answer

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Question 10

A fair coin is flipped 10 times. What is the probability of getting exactly 7 heads? (Use the binomial formula: $$P(X = k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$, where n=10$, k=7$, p=0.5$)

Accepted Answer

$$P(X=7) = \binom{10}{7} (0.5)^7$ (0.5)^3$

Question 11

Which of the following is a requirement for a random variable to be considered binomial?

Accepted Answer

There are a fixed number of trials, each with two possible outcomes.

Question 12

The expected value $$E(X) of a $$discrete probability distribution is best described as:

Accepted Answer

The long-run average value of the random variable after many trials.

Question 13

A normal distribution is fully characterized by which two parameters?

Accepted Answer

Mean and standard deviation

Question 14

If $$P(A|B) = \frac{P(A \cap B)}{P(B)}$$, what does $$P(A|B)$$ represent?

Accepted Answer

The probability of event A occurring given that event B has occurred.

Question 15

A study finds a strong positive linear relationship between hours studied and exam scores. Which of the following best describes this relationship?

Accepted Answer

As hours studied increase, exam scores tend to increase.

Question 16

Which of the following is TRUE about the law of large numbers?

Accepted Answer

As the number of trials increases, the observed proportion approaches the theoretical probability.

Question 17

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

Accepted Answer

The height of students in a classroom.

Question 18

A researcher is interested in whether there is an association between gender (male/female) and preference for a new product (like/dislike). Which statistical tool should they use to analyze the data?

Accepted Answer

Two-way table and conditional proportions

Question 19

If two events are independent, which of the following is true?

Accepted Answer

$$P(A \cap B) = P(A) 	imes P(B)$$

Question 20

A pharmaceutical company tests a new drug on 1000 patients and finds that 200 experience side effects. What is the empirical probability that a patient will experience side effects?

Accepted Answer

$$0.2$$

Statistics Study Guide: Key Concepts and Methods

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