Q: If two events $$A$$ and $$B$$ are independent, which of the following is true?

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

Question 1

Given the regression equation $$y = 3x + 2$$, what is the predicted value of $$y$$ when $$x = 5$$?

Accepted Answer

$$y = 17$$

Question 2

Which of the following best describes the coefficient of determination ($$R^2) in a $$regression analysis?

Accepted Answer

It measures the proportion of variability in the dependent variable explained by the independent variable.

Question 3

A researcher wants to estimate the average height of university students. Which sampling method is most likely to produce a representative sample?

Accepted Answer

Simple random sampling

Question 4

Which statement about the Law of Large Numbers is correct?

Accepted Answer

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

Question 5

If the probability of event $$A is$$ $$0.3$$ and the probability of event $$B is$$ $$0.5$$, and $$A$$ and $$B$$ are mutually exclusive, what is the probability that either $$A or$$ $$B$$ occurs?

Accepted Answer

$$P(A \cup B) = 0.8$$

Question 6

A coin is flipped 75 times. What is the expected number of heads?

Accepted Answer

$$37.5$$

Question 7

Which of the following is NOT a requirement for using the Normal distribution to approximate the sampling distribution of a proportion?

Accepted Answer

The sample size must be less than 30.

Question 8

A study finds a correlation coefficient $$r = 0.85$$ between hours studied and exam score. What does this imply?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam score.

Question 9

If a 95% confidence interval for a population proportion is $$(0.40, 0.60)$$, which of the following statements is correct?

Accepted Answer

We are 95% confident that the true population proportion is between 0.40 and 0.60.

Question 10

Which of the following would increase the margin of error in a confidence interval for a proportion?

Accepted Answer

Decreasing the sample size

Question 11

A medical researcher wants to determine if a new drug is effective. She randomly assigns patients to receive either the drug or a placebo. What type of study is this?

Accepted Answer

Experiment

Question 12

If two events $$A$$ and $$B$$ are independent, which of the following is true?

Accepted Answer

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

Question 13

A city council wants to estimate the proportion of residents who support a new law. They survey 1000 randomly selected residents and find that 420 support the law. What is the sample proportion?

Accepted Answer

$$\hat{p} = 0.42$$

Question 14

Which of the following is a potential weakness of an observational study compared to an experiment?

Accepted Answer

It is more difficult to establish causation.

Question 15

If the standard deviation of a population is $$\sigma = 10$$ and the sample size is $$n = 25$$, what is the standard error of the mean?

Accepted Answer

$$2$$

Question 16

Which of the following best describes a simple random sample?

Accepted Answer

Every member of the population has an equal chance of being selected.

Question 17

A student rolls a fair six-sided die 60 times. What is the expected number of times a '4' will appear?

Accepted Answer

$$10$$

Question 18

Which of the following is true about the margin of error in a confidence interval?

Accepted Answer

Increasing the sample size decreases the margin of error.

Question 19

If $$P(A) = 0.4$$ and $$P(B) = 0.3$$, and $$A$$ and $$B$$ are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.12$$

Question 20

A sample of 100 students has a mean test score of 75 and a standard deviation of 10. What is the standard error of the mean?

Accepted Answer

$$1$$

Statistics Exam 2 Study Guide: Regression, Sampling, Probability, and Confidence Intervals

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