Probability and Statistics Quizzes: Test Your Skills

Question 1

When rolling a standard six-sided die, which number is NOT a possible outcome?

Accepted Answer

7

Answer

1

Answer

3

Answer

5

Question 2

Which of the following measures the spread or variability of a data set?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 3

A survey of 100 students found that 60% own a smartphone. What is the probability that a randomly selected student does NOT own a smartphone?

Accepted Answer

0.4

Answer

0.6

Answer

1

Answer

0.25

Question 4

Which sampling method ensures that every individual in the population has an equal chance of being selected?

Accepted Answer

Simple random sampling

Answer

Stratified sampling

Answer

Cluster sampling

Answer

Quota sampling

Question 5

What action will widen the range of a confidence interval?

Accepted Answer

Increasing the confidence level

Answer

Increasing the sample size

Answer

Decreasing the variability of the population

Answer

Decreasing the sample mean

Question 6

A scatter plot shows a negative correlation between two variables. What does this indicate?

Accepted Answer

As one variable increases, the other decreases.

Answer

As one variable increases, the other also increases.

Answer

There is no relationship between the two variables.

Answer

The two variables are inversely proportional.

Question 7

Which statistical test is used to compare the means of two independent groups?

Accepted Answer

t-test

Answer

ANOVA

Answer

Chi-square test

Answer

Regression analysis

Question 8

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If a marble is randomly drawn, what is the probability of picking a blue marble?

Accepted Answer

3 in 10

Answer

1 in 5

Answer

1 in 3

Answer

1 in 2

Question 9

Which of the following is NOT a way to measure the center of a data set?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 10

Which sampling method provides an equal chance for every individual in the population to be included?

Accepted Answer

Simple random sampling

Answer

Convenience sampling

Answer

Quota sampling

Answer

Stratified sampling

Question 11

Which statistical test is used to determine if there is a difference in means between two independent populations?

Accepted Answer

Two-sample t-test

Answer

One-sample t-test

Answer

ANOVA

Answer

Chi-square test

Question 12

In a medical study, why is a placebo group included?

Accepted Answer

To compare the effects of the treatment

Answer

To ensure no side effects exist

Answer

To increase the sample size

Answer

To lower the cost of the study

Question 13

Which of the following is a measure of dispersion?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 14

A data set has a mean of 20 and a standard deviation of 4. If a data point with a value of 12 is added, what is the new mean of the data set?

Accepted Answer

19

Answer

18

Answer

20

Answer

21

Question 15

A study found a strong correlation between exercise and health outcomes. This means that:

Accepted Answer

People who exercise are generally healthier than those who do not.

Answer

Exercise directly causes good health outcomes.

Answer

The relationship between exercise and health outcomes is perfectly linear.

Answer

Exercise is the only factor that affects health outcomes.

Question 16

In hypothesis testing, what is the purpose of the null hypothesis?

Accepted Answer

To represent the claim that there is no significant difference or effect.

Answer

To be proven false.

Answer

To be known as true.

Question 17

The probability of event A happening is 0.4. If event A occurs, the probability of event B happening is 0.6. What's the probability of both events happening?

Accepted Answer

0.24

Answer

0.4

Answer

0.6

Answer

0

Question 18

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of selecting a blue marble?

Accepted Answer

3/10

Answer

1/5

Answer

1/2

Answer

2/5

Question 19

What type of graph is used to depict the distribution of data?

Accepted Answer

Histogram

Answer

Bar graph

Answer

Pie chart

Answer

Scatter plot

Question 20

What is the distinction between a population and a sample?

Accepted Answer

A sample is a subset of a population.

Answer

A population is smaller than a sample.

Answer

A sample is smaller than a population.

Answer

A population is always the same as a sample.

Question 21

What is the purpose of a confidence interval?

Accepted Answer

To estimate the population mean

Answer

To test a hypothesis

Answer

To make predictions

Answer

To calculate the probability of an event

Question 22

In a research study, what is the primary purpose of a control group?

Accepted Answer

To provide a baseline for comparison

Answer

To receive the treatment or intervention

Answer

To be randomly selected

Answer

To be larger than the experimental group

Question 23

A statistics teacher randomly measures 10 students and finds their average height to be 65 inches. What is the sample size?

Accepted Answer

10

Answer

5

Answer

15

Answer

20

Question 24

Which measure of central tendency is most significantly affected by outliers?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Range

Question 25

A dataset has a range of 10 and a mean of 5. What is the greatest possible value in the dataset?

Accepted Answer

15

Answer

5

Answer

10

Answer

20

Question 26

A scatterplot displays a strong positive correlation between two variables. What can be concluded from this?

Accepted Answer

As one variable increases, the other tends to increase.

Answer

As one variable increases, the other tends to decrease.

Answer

There is no relationship between the two variables.

Answer

The relationship between the two variables is non-linear.

Question 27

A histogram shows a distribution that is skewed to the left. What does this indicate?

Accepted Answer

The majority of values are below the mean.

Answer

The majority of values are close to the mean.

Answer

The distribution is uniform.

Answer

There is no information about the distribution from the histogram.

Question 28

A data set has a mean of 10 and a standard deviation of 2. If a new value of 15 is added to the data set, what will be the new mean?

Accepted Answer

11

Answer

10.2

Answer

10.5

Answer

11.5

Question 29

A histogram shows the distribution of test scores in a class. The histogram has a bell-shaped curve. Which conclusion can be drawn from this?

Accepted Answer

The majority of the scores are close to the mean.

Answer

The scores are evenly distributed across the range.

Answer

The highest score is significantly higher than the mean.

Answer

The lowest score is significantly lower than the mean.

Question 30

A scatterplot shows a positive correlation between two variables. This means that:

Accepted Answer

As one variable increases, the other variable also increases.

Answer

As one variable increases, the other variable decreases.

Answer

As one variable increases, the other variable stays the same.

Answer

There is no relationship between the two variables.

Question 31

A regression line is used to:

Accepted Answer

Predict the value of one variable based on the value of another variable.

Answer

Describe the shape of a data set.

Answer

Compare the means of two data sets.

Answer

Determine the probability of an event.

Question 32

A hypothesis test is used to:

Accepted Answer

Determine whether there is a significant difference between two groups.

Answer

Predict the outcome of a future event.

Answer

Calculate the probability of an event.

Answer

Describe the shape of a data set.

Question 33

A confidence interval is used to:

Accepted Answer

Estimate the true mean of a population based on a sample.

Answer

Determine whether there is a significant difference between two groups.

Answer

Predict the outcome of a future event.

Answer

Calculate the probability of an event.

Question 34

Which statement accurately describes the relationship between correlation and causation?

Accepted Answer

Causation implies correlation, while correlation does not imply causation.

Answer

Correlation implies causation, but causation does not imply correlation.

Answer

Correlation and causation are interchangeable concepts.

Answer

Causation can be definitively proven using only correlation data.

Question 35

A survey of 100 students revealed that 60 students like math, 70 students like science, and 40 students like both math and science. What is the probability that a randomly selected student likes science, given that they like math?

Accepted Answer

2/3

Answer

1/3

Answer

1/4

Answer

1/2

Question 36

In a survey of 100 students, 60% liked math. If another 120 students are surveyed, how many are expected to like math?

Accepted Answer

72

Answer

60

Answer

80

Answer

90

Question 37

A researcher wants to compare the effectiveness of two teaching methods. They randomly assign 50 students to each method and find that the first method has an average score of 75 and the second method has an average score of 80. Which statistical test would be appropriate to determine if the difference in scores is statistically significant?

Accepted Answer

Independent samples t-test

Answer

One-sample t-test

Answer

Regression analysis

Answer

Chi-square test

Question 38

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of randomly selecting a blue marble?

Accepted Answer

3/10

Answer

1/3

Answer

2/5

Answer

1/4

Question 39

A coin is flipped 5 times. What is the probability of getting at least one head?

Accepted Answer

31/32

Answer

1/5

Answer

1/2

Answer

1/31

Question 40

A box contains 6 blue pencils, 5 red pencils, and 3 green pencils. Two pencils are randomly selected one after another without replacement. What is the probability that the first pencil selected is blue and the second pencil is red?

Accepted Answer

5/33

Answer

1/3

Answer

2/11

Answer

1/6

Question 41

The average (mean) of a set of numbers is 10. If one more number with a value of 15 is added to the set, what is the new mean?

Accepted Answer

10.5

Answer

10

Answer

11

Answer

15

Question 42

A correlation coefficient of 0.8 indicates a:

Accepted Answer

Strong positive correlation

Answer

Weak positive correlation

Answer

No correlation

Question 43

Which sampling method ensures that every member of the population has an equal chance of being selected?

Accepted Answer

Simple random sampling

Answer

Stratified sampling

Answer

Quota sampling

Answer

Convenience sampling

Question 44

A hypothesis test results in a p-value of 0.04. Based on a significance level of 0.05, what should we conclude?

Accepted Answer

Reject the null hypothesis

Answer

Cannot conclude

Answer

Accept the null hypothesis

Answer

Need more data

Question 45

A confidence interval provides an estimate of the true population parameter with a certain:

Accepted Answer

Level of confidence

Answer

Population standard deviation

Answer

Sample mean

Question 46

A fair coin is flipped three times. What is the probability of getting at least one head?

Accepted Answer

7/8

Answer

1/4

Answer

1/2

Answer

3/4

Question 47

A music teacher wants to form a group of 4 students out of a class of 12 students. How many different groups can she form?

Accepted Answer

495

Answer

792

Answer

277

Question 48

A survey of 200 people found that 120 of them watch the morning news. If 10 people are randomly selected from this group, what is the probability that exactly half of them watch the morning news?

Accepted Answer

0.246

Answer

0.50

Answer

0.08

Question 49

Which of the following is not considered a measure of central tendency?

Accepted Answer

Range

Answer

Median

Answer

Mode

Answer

Mean

Question 50

A coin is flipped twice. What is the probability of getting a head on at least one flip?

Accepted Answer

3/4

Answer

1/4

Answer

1/2

Answer

0

Question 51

A bag contains 2 red marbles and 5 blue marbles. What is the probability of randomly drawing a red marble?

Accepted Answer

2/7

Answer

1/7

Answer

5/7

Answer

1/3

Question 52

The mean of a dataset is 25. If a new data point of 30 is added, what will happen to the mean?

Accepted Answer

The mean will increase.

Answer

The mean will decrease.

Answer

It's impossible to determine.

Answer

The mean will stay the same.

Question 53

A dataset has a standard deviation of 10. What does this indicate about the data?

Accepted Answer

The data is spread out, on average, 10 units from the mean.

Answer

The data is clustered closely around the mean.

Answer

The data points are all equal to 10.

Question 54

Which of the following is NOT a measure of central tendency?

Accepted Answer

Range

Answer

Mean

Answer

Median

Question 55

In an experiment, the group that receives the treatment being tested is called the:

Accepted Answer

Experimental group

Answer

Control group

Answer

Random group

Answer

Placebo group

Question 56

A correlation coefficient of 0.9 indicates:

Accepted Answer

A strong positive linear relationship between two variables.

Answer

A weak negative linear relationship between two variables.

Answer

No linear relationship between two variables.

Answer

A strong negative linear relationship between two variables.