Q: If events $$A$$ and $$B$$ are independent, which formula correctly gives $$P(A \text{ and } B)$$?

$$P(A \text{ and } B) = P(A) \times P(B)$$

Question 1

Which of the following best describes a parameter in statistics?

Accepted Answer

A numerical summary calculated from a population.

Question 2

A researcher wants to study the average height of all university students. She randomly selects 100 students and calculates their average height. In this scenario, which is the population and which is the sample?

Accepted Answer

Population: all university students; Sample: 100 students.

Question 3

Which of the following is NOT a measure of spread?

Accepted Answer

Median

Question 4

A histogram of exam scores shows a distribution that is right-skewed. Which measure of center is most affected by the skewness?

Accepted Answer

Mean

Question 5

Given the five-number summary: Minimum = 10, Q1 = 20, Median = 30, Q3 = 40, Maximum = 50, what is the interquartile range (IQR)?

$$	ext{IQR} = Q_3$ - Q_1$

Accepted Answer

$$	ext{IQR} = 20$$

Question 6

Which of the following statements about the correlation coefficient $$r is $$TRUE?

Accepted Answer

$$r$$ describes the strength and direction of a linear relationship.

Question 7

A regression line is given by $$\hat{y} = 2 + 3x. $$What is the predicted value of $$y$$ when $$x = 4$$?

Accepted Answer

$$\hat{y} = 14$$

Question 8

In a medical study, the sensitivity of a test is defined as $$P(	ext{POS}|S). $$What does this represent?

Accepted Answer

The probability the test is positive given the subject has the disease.

Question 9

A random variable $$X$$ has the following probability distribution: $$P(X=1)=0.2$$, $$P(X=2)=0.5$$, $$P(X=3)=0.3. $$What is the expected value (mean) of $$X$$?

$$\mu = \sum x P(x)$$

Accepted Answer

$$\mu = 2.1$$

Question 10

A normal distribution has mean $$\mu = 100$$ and standard deviation $$\sigma = 15. $$What is the $$z-$$score for an observation $$x = 130$$?

$$z = \frac{x - \mu}{\sigma}$$

Accepted Answer

$$z = 2$$

Question 11

Which sampling method is most likely to produce a representative sample of a population?

Accepted Answer

Simple random sample

Question 12

In a binomial experiment with $$n = 10$$ trials and $$p = 0.3$$, what is the mean number of successes?

$$	ext{Mean} = np$$

Accepted Answer

$$3$$

Question 13

Which of the following is an example of a lurking variable?

Accepted Answer

A variable that affects the response but is not included in the analysis.

Question 14

A contingency table is used to analyze:

Accepted Answer

The relationship between two categorical variables.

Question 15

If events $$A$$ and $$B$$ are independent, which formula correctly gives $$P(A 	ext{ and } B)$$?

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B)$$

Question 16

A study follows a group of patients over several years to observe the development of a disease. What type of study is this?

Accepted Answer

Prospective study

Question 17

In a box-and-whisker plot, which value is NOT part of the five-number summary?

Accepted Answer

Mean

Question 18

A survey is conducted by asking people at a shopping mall about their opinions on a new product. Which type of sampling is this?

Accepted Answer

Convenience sample

Question 19

If the probability of event $$A is$$ $$0.7$$, what is the probability of the complement of $$A$$?

$$P(A^C) = 1 - P(A)$$

Accepted Answer

$$0.3$$

Question 20

A researcher wants to estimate the proportion of voters who support a candidate. She uses a random sample of 400 voters. What is the margin of error for her estimate?

$$	ext{Margin of error} = \frac{1}{\sqrt{n}}$$

Accepted Answer

$$0.05$$

STA 2023 Exam 1 Review: Introductory Statistics Study Guide

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