Question 1

Which of the following best describes the primary purpose of statistics in research?

Accepted Answer

To analyze, interpret, and present data to reach reasonable conclusions.

Question 2

A researcher wants to study the effect of a new medication on blood pressure. Which of the following best represents a random sample?

Accepted Answer

Selecting every 10th patient from a list of all patients at a hospital.

Question 3

Which of the following is a discrete random variable?

Accepted Answer

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

Question 4

Given a normal distribution with mean $$\mu = 100$$ and standard deviation $$\sigma = 15$$, what is the $$z-$$score for a value of $$130$$?

Accepted Answer

$$z = \frac{130 - 100}{15} = 2$$

Question 5

Which of the following statements about mutually exclusive events is correct?

Accepted Answer

If events $$A$$ and $$B$$ are mutually exclusive, then $$P(A \cap B) = 0.$$

Question 6

A box plot is useful for which of the following purposes?

Accepted Answer

Displaying the distribution, median, and potential outliers of a data set.

Question 7

If the probability of event $$A is$$ $$0.3$$ and the probability of event $$B is$$ $$0.5$$, and $$A$$ and $$B$$ are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$P(A \cap B) = 0.15$$

Question 8

Which formula is used to calculate the confidence interval for a population mean when the population standard deviation is known?

Accepted Answer

$$\bar{x} \pm z^* \frac{\sigma}{\sqrt{n}}$$

Question 9

A researcher tests the null hypothesis $$H_0$$: \mu = 50$$ against the alternative H_a$$: \mu 
eq 50$$. The sample mean is 54$, the population standard deviation is 8$, and the sample size is 16$. What is the test statistic?

Accepted Answer

$$z = \frac{54 - 50}{8/\sqrt{16}} = 2$$

Question 10

Which of the following best describes the relationship between correlation and causation?

Accepted Answer

Correlation does not imply causation.

Question 11

A fair coin is flipped 10 times. What is the probability of getting exactly 6 heads? (Use the binomial formula)

Accepted Answer

$$P(X=6) = \binom{10}{6} (0.5)^6$ (0.5)^4$

Question 12

Which measure of central tendency is most affected by extreme values (outliers)?

Accepted Answer

Mean

Question 13

A histogram is best used to:

Accepted Answer

Display the distribution of a single quantitative variable.

Question 14

Which of the following is the correct formula for the sample variance $$s^2$$?

Accepted Answer

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

Question 15

If a data set is skewed to the right, which of the following is most likely true?

Accepted Answer

Mode \u003c Median \u003c Mean

Question 16

Which of the following is NOT a requirement for a binomial experiment?

Accepted Answer

The probability of success changes from trial to trial.

Question 17

A researcher wants to estimate the proportion of students who own a smartphone. Which formula should be used to calculate the confidence interval for a population proportion?

Accepted Answer

$$\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 18

Which of the following best describes the null hypothesis in hypothesis testing?

Accepted Answer

A statement that there is no effect or difference.

Question 19

In a linear regression analysis, what does the slope of the regression line represent?

Accepted Answer

The change in $$y$$ for a one-unit increase in $$x.$$

Question 20

Which of the following is an example of an ethical issue in experimental design?

Accepted Answer

Failing to obtain informed consent from participants.

Elementary Statistical Methods: Course Structure and Study Guide

Study Guide - Practice Questions

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