Free DSST Principles of Statistics Practice Test (2026)

Question 1

A regression of monthly sales (in thousands of dollars) on advertising spending (in thousands of dollars) gives ŷ = 12 + 3.5x. How should the slope be interpreted?

Accepted Answer

Each additional $1,000 in advertising is associated with about $3,500 more in predicted sales.

Answer

Each additional $1 in advertising is associated with about $3.50 less in predicted sales.

Answer

Predicted sales are $12,000 more for each additional $3,500 spent on advertising.

Answer

Sales would be about $3,500 if the company spent nothing at all on advertising.

Question 2

A data set has a first quartile of 20 and a third quartile of 32. Using the 1.5 × IQR rule, which of these values is an outlier?

Accepted Answer

52

Answer

4

Answer

15

Answer

48

Question 3

The correlation between study time and exam score is r = 0.6. What proportion of the variation in exam scores is explained by the linear relationship with study time?

Accepted Answer

0.36

Answer

0.60

Answer

0.64

Answer

0.77

Question 4

Which statement correctly describes the central limit theorem?

Accepted Answer

For large n, the distribution of sample means is about normal, whatever the population's shape.

Answer

For large n, the population itself becomes approximately normal, whatever its original shape.

Answer

For large n, every individual observation in the sample will be close to the population mean.

Answer

For large n, the sample standard deviation shrinks toward zero as more data are collected.

Question 5

Runners' finishing positions in a race (1st, 2nd, 3rd, and so on) are measured on which scale?

Accepted Answer

Ordinal

Answer

Nominal

Answer

Interval

Answer

Ratio

Question 6

A regression line predicts a score of 70 for a student who actually scored 76. What is the residual?

Accepted Answer

6

Answer

−6

Answer

26

Answer

70

Question 7

A multiple-choice quiz has 5 questions, each with a 0.2 chance of being guessed correctly. What is the probability of guessing exactly 2 correctly?

Accepted Answer

0.2048

Answer

0.0205

Answer

0.0400

Answer

0.4000

Question 8

By what factor must the sample size be multiplied to cut the standard error of the mean in half?

Accepted Answer

4

Answer

2

Answer

8

Answer

16

Question 9

To test H₀: p = 0.5, a researcher surveys 100 people and finds that 60 favor a proposal. What is the test statistic?

Accepted Answer

z = 2.00

Answer

z = 0.20

Answer

z = 1.00

Answer

z = 4.00

Question 10

P(A) = 0.3, P(B) = 0.5 and P(A and B) = 0.15. Which statement is true?

Accepted Answer

A and B are independent but not mutually exclusive.

Answer

A and B are mutually exclusive but not independent.

Answer

A and B are both independent and mutually exclusive.

Answer

A and B are neither independent nor mutually exclusive.

Question 11

Test scores are normally distributed with mean 70 and standard deviation 8. About what proportion of scores lie between 62 and 86?

Accepted Answer

0.8185

Answer

0.1587

Answer

0.6826

Answer

0.9772

Question 12

A committee of 2 is chosen at random from 5 women and 3 men. What is the probability that both members are women?

Accepted Answer

0.357

Answer

0.107

Answer

0.391

Answer

0.625

Question 13

A test of H₀: μ = 100 at the 0.05 significance level gives a p-value of 0.03. What is the correct decision?

Accepted Answer

Reject H₀, because the p-value is less than 0.05

Answer

Fail to reject H₀, because the p-value is less than 0.05

Answer

Accept H₀ as proven true, because the p-value is small

Answer

Reject H₀, because the p-value is greater than 0.01

Question 14

P(A) = 0.5, P(B) = 0.4 and P(A and B) = 0.2. What is P(A or B)?

Accepted Answer

0.70

Answer

0.20

Answer

0.50

Answer

0.90

Question 15

A researcher wants to compare the mean yields of three fertilizer types in one test. Which procedure is most appropriate?

Accepted Answer

One-way analysis of variance (ANOVA)

Answer

A chi-square test of independence

Answer

A paired t-test

Answer

Simple linear regression

Question 16

A university divides its students by class year and then randomly selects 50 students from each year. Which sampling method is this?

Accepted Answer

Stratified random sampling

Answer

Cluster sampling

Answer

Systematic sampling

Answer

Convenience sampling

Question 17

A chi-square test of independence uses a contingency table with 3 rows and 4 columns. How many degrees of freedom does the test have?

Accepted Answer

6

Answer

5

Answer

7

Answer

12

Question 18

Researchers review the records of 5,000 adults and find that those who drink more coffee report fewer headaches. What can they conclude?

Accepted Answer

The two are associated, but the study cannot show that coffee prevents headaches.

Answer

Drinking more coffee causes people to have fewer headaches each month.

Answer

Having fewer headaches causes people to drink more coffee each day.

Answer

There is no relationship at all, because the study was not an experiment.

Question 19

A random sample of 36 has a mean of 50, and the population standard deviation is known to be 12. What is the 95% confidence interval for the population mean?

Accepted Answer

46.08 to 53.92

Answer

48.04 to 51.96

Answer

46.71 to 53.29

Answer

26.48 to 73.52

Question 20

For the data set 2, 4, 4, 5, 7, 9, 40, which statement is correct?

Accepted Answer

The mean is greater than the median, and the data are skewed right.

Answer

The mean is less than the median, and the data are skewed left.

Answer

The mean equals the median, so the data are symmetric.

Answer

The mean is greater than the median, and the data are skewed left.

Question 21

Holding everything else constant, which change increases the power of a hypothesis test?

Accepted Answer

Increasing the sample size

Answer

Lowering the significance level from 0.05 to 0.01

Answer

Using a smaller sample

Answer

Increasing the variability of the data

Question 22

A population has mean 50 and standard deviation 16. For random samples of size 64, what is the probability that the sample mean exceeds 53?

Accepted Answer

0.0668

Answer

0.4256

Answer

0.4332

Answer

0.9332

Question 23

In hypothesis testing, a Type I error occurs when a researcher

Accepted Answer

rejects a null hypothesis that is actually true

Answer

fails to reject a null hypothesis that is actually false

Answer

rejects a null hypothesis that is actually false

Answer

uses a sample size that is too small to detect any effect

Question 24

A study finds a correlation of r = −0.85 between hours of television watched per week and test scores. Which statement is the best interpretation?

Accepted Answer

There is a strong negative linear relationship between the two variables.

Answer

Watching television causes test scores to fall.

Answer

There is a weak negative linear relationship between the two variables.

Answer

About 85% of students who watch more television score lower.

Question 25

A raffle sells 500 tickets at $2 each, and one ticket wins a $400 prize. What is the expected value of buying one ticket?

Accepted Answer

−$1.20

Answer

−$2.00

Answer

−$0.80

Answer

$0.80

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