Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a numerical summary of a population, while a statistic is a numerical summary of a sample.

Question 2

A researcher wants to estimate the average height of all university students. She randomly selects 100 students and calculates their mean height. Which of the following is the best description of the mean height she calculated?

Accepted Answer

It is a statistic because it is calculated from a sample.

Question 3

Which of the following is NOT a property of the normal distribution?

Accepted Answer

It is skewed to the right.

Question 4

Suppose the probability that a randomly selected person has blood type O is 0.45. If two people are selected independently, what is the probability that both have blood type O?

Accepted Answer

$$0.45 	imes 0.45$$

Question 5

A fair six-sided die is rolled twice. What is the probability that both rolls result in an even number?

Accepted Answer

$$\frac{1}{4}$$

Question 6

Which of the following statements about the Central Limit Theorem is TRUE?

Accepted Answer

The sampling distribution of the sample mean will be approximately normal if the sample size is large enough, regardless of the population distribution.

Question 7

A 95% confidence interval for a population mean is calculated as $$(12.5, 17.5). $$Which of the following is the correct interpretation?

Accepted Answer

We are 95% confident that the population mean is between 12.5 and 17.5.

Question 8

Which of the following is the correct formula for the standard error of the sample mean when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$\frac{\sigma}{\sqrt{n}}$$

Question 9

A study tests whether a new medication lowers blood pressure compared to a placebo. The null hypothesis is $$H_0$$: \mu = 0$$ (no effect). The p-value is found to be 0.03. At a significance level of $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Reject $$H_0$$; there is evidence that the medication lowers blood pressure.

Question 10

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis.

Question 11

A contingency table is used to:

Accepted Answer

Summarize the relationship between two categorical variables.

Question 12

Which of the following is the correct formula for the probability of the union of two events $$A$$ and $$B$$?

Accepted Answer

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

Question 13

Suppose a sample of 36 students has a mean test score of 80 and a standard deviation of 12. What is the standard error of the mean?

Accepted Answer

$$2$$

Question 14

Which of the following is a requirement for using the one-sample $$t-$$test for a mean?

Accepted Answer

The sample must be randomly selected from a normally distributed population.

Question 15

A researcher wants to compare the mean cholesterol levels between two independent groups. Which statistical test should be used?

Accepted Answer

Two-sample $$t-$$test

Question 16

Which of the following is the correct formula for the confidence interval for a population mean when the population standard deviation is unknown?

Accepted Answer

$$\bar{x} \pm t^* \frac{s}{\sqrt{n}}$$

Question 17

Which of the following best describes the purpose of ANOVA (Analysis of Variance)?

Accepted Answer

To compare the means of three or more groups.

Question 18

If the correlation coefficient $$r$$ between two variables is $$-0.85$$, what does this indicate?

Accepted Answer

There is a strong negative linear relationship.

Question 19

Which of the following is a correct interpretation of a $$p-$$value in hypothesis testing?

Accepted Answer

The probability of obtaining a result as extreme or more extreme than the observed result, assuming the null hypothesis is true.

Question 20

A researcher is interested in the relationship between hours studied and exam scores. She calculates the regression equation $$\hat{y} = 50 + 5x. $$What is the predicted exam score for a student who studies 6 hours?

Accepted Answer

$$80$$

Statistics Final Exam Review: Core Concepts and Methods

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