Probability and Statistics Quizzes for Sixth Form College Year 12

Question 1

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

Accepted Answer

7/10

Answer

1/2

Answer

5/10

Answer

9/10

Question 2

A correlation coefficient of -0.8 between two variables indicates what type of relationship?

Accepted Answer

Strong negative correlation

Answer

Strong positive correlation

Answer

Weak negative correlation

Answer

No correlation

Question 3

A scatterplot exhibits a positive linear relationship between two variables. What does this imply?

Accepted Answer

As one variable increases, the other also increases.

Answer

As one variable decreases, the other increases.

Answer

There is no relationship between the variables.

Answer

The variables are inversely proportional.

Question 4

A fair six-sided die is rolled twice. What is the probability that the sum of the numbers on the two rolls is 7?

Accepted Answer

1/12

Answer

1/3

Answer

1/6

Answer

1/36

Question 5

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

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 6

Which sampling method ensures equal chances of selection for all population members?

Accepted Answer

Simple random sampling

Answer

Stratified sampling

Answer

Cluster sampling

Answer

Convenience sampling

Question 7

In a chi-square test of independence, what is the null hypothesis?

Accepted Answer

The variables are independent.

Answer

The variables are not independent.

Answer

The variables are negatively correlated.

Answer

The variables are positively correlated.

Question 8

Which non-parametric test can be used to compare the medians of two independent groups?

Accepted Answer

Mann-Whitney U test

Answer

t-test

Answer

ANOVA

Answer

Chi-square test

Question 9

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

Accepted Answer

Mean less than or equal to median

Answer

Symmetrical

Answer

Bell-shaped

Answer

Tails approach the horizontal asymptotes

Question 10

Which of the following is a non-parametric test?

Accepted Answer

Spearman's rank correlation coefficient

Answer

t-test

Answer

Pearson's correlation coefficient

Answer

ANOVA

Question 11

From a bag containing 5 red, 3 blue, and 2 green balls, if one ball is drawn at random, what is the probability of drawing a blue ball?

Accepted Answer

1:3

Answer

1:5

Answer

1:2

Answer

1:4

Question 12

When fitting a linear regression model to data, a coefficient of determination (R-squared) of 0.85 is obtained. What does this value imply?

Accepted Answer

85% of the dependent variable's variation is explained by the independent variable.

Answer

85% of the data points lie on the regression line.

Answer

The model is a poor fit.

Answer

The regression line has a slope of 0.85.

Question 13

If a scatterplot exhibits a strong positive correlation between study hours and exam scores, what can be inferred?

Accepted Answer

Higher study hours tend to lead to higher exam scores.

Answer

Higher study hours tend to lead to lower exam scores.

Answer

There is no relationship between study hours and exam scores.

Answer

Exam scores are independent of study hours.

Question 14

A scatter plot is a graphical representation of the relationship between two variables.

Accepted Answer

True

Answer

False

Question 15

A correlation coefficient quantifies the strength and direction of the linear relationship between two variables.

Accepted Answer

True

Answer

False

Question 16

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

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 17

The probability of rolling a 6 on a fair six-sided dice is:

Accepted Answer

1/6

Answer

1/4

Answer

1/5

Answer

1/3

Question 18

Which of the following are parameters of a normal distribution?

Accepted Answer

Mean and standard deviation

Answer

Median and mode

Answer

Skewness and kurtosis

Answer

Both (A) and (C)

Question 19

A hypothesis test is conducted with a significance level of 0.05. If the p-value is 0.06, what is the appropriate conclusion?

Accepted Answer

Fail to reject the null hypothesis

Answer

Reject the null hypothesis

Answer

Accept the alternative hypothesis

Answer

Insufficient information

Question 20

The correlation coefficient between two variables can range from:

Accepted Answer

-1 to 1

Answer

-1 to 0

Answer

0 to 1

Answer

0 to 2

Question 21

The standard deviation of a sample is a measure of:

Accepted Answer

Spread

Answer

Central tendency

Answer

Skewness

Answer

Kurtosis

Question 22

Which probability distribution characterizes the number of successes within a sequence of independent trials?

Accepted Answer

Binomial distribution

Answer

Normal distribution

Answer

Poisson distribution

Answer

Geometric distribution

Question 23

Which measure of central tendency remains unaffected by outliers?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 24

For comparing the means of two independent populations, which hypothesis test is appropriate?

Accepted Answer

Two-sample t-test

Answer

One-sample t-test

Answer

Chi-square test

Answer

F-test

Question 25

Which graphical representation effectively displays the relationship between two variables?

Accepted Answer

Scatter plot

Answer

Bar chart

Answer

Pie chart

Answer

Histogram

Question 26

In the context of a perfect positive linear relationship between two variables, what is the correlation coefficient?

Accepted Answer

1

Answer

0

Answer

0.5

Answer

-1

Question 27

Which sampling method ensures an equal chance of selection for every member of the population?

Accepted Answer

Simple random sampling

Answer

Convenience sampling

Answer

Quota sampling

Answer

Stratified sampling

Question 28

A fair coin is tossed twice. What is the probability of obtaining tails on both tosses?

Accepted Answer

0.25

Answer

0.5

Answer

0.75

Answer

1

Question 29

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

Accepted Answer

Random sampling

Answer

Convenience sampling

Answer

Stratified sampling

Answer

Cluster sampling

Question 30

What is the difference between a population and a sample?

Accepted Answer

A sample is a subset of a population.

Answer

A population is a subset of a sample.

Answer

A population and a sample are the same thing.

Answer

A sample is always larger than a population.

Question 31

Which of the following is NOT a possible outcome when rolling a standard six-sided die?

Accepted Answer

7

Answer

1

Answer

3

Answer

5

Question 32

A fair coin is tossed 5 times. What is the probability of getting exactly 3 heads?

Accepted Answer

10/32

Answer

1/4

Answer

5/16

Answer

1/8

Question 33

Which of the following best describes the purpose of a mean?

Accepted Answer

To measure the central tendency of a dataset

Answer

To estimate the likelihood of an event occurring

Answer

To test whether there is a significant difference between groups

Answer

To predict future values based on past data

Question 34

Which of the following is the first step in hypothesis testing?

Accepted Answer

Stating the null and alternative hypotheses

Answer

Collecting data from a sample

Answer

Calculating the p-value

Answer

Making a decision about the hypothesis

Question 35

In hypothesis testing, the null hypothesis typically represents the assumption that:

Accepted Answer

There is no significant difference between groups or variables

Answer

The population mean is equal to a specific value

Answer

The sample mean is equal to the population mean

Answer

The correlation coefficient is greater than 0.5

Question 36

Which of the following errors occurs when we reject the null hypothesis when it is actually true?

Accepted Answer

Type I error

Answer

Type II error

Answer

Sampling error

Answer

Measurement error

Question 37

What is a primary goal of constructing a confidence interval?

Accepted Answer

To estimate a population parameter with a specified level of confidence

Answer

To test whether there is a significant difference between means

Answer

To determine the probability of an event occurring

Answer

To predict future values based on a regression model

Question 38

Which of the following accurately describes the standard deviation of a data set?

Accepted Answer

A measure of how spread out the data is

Answer

The average value of the data

Answer

The probability of an event occurring

Answer

The correlation between two variables

Question 39

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

Accepted Answer

It represents the hypothesis assumed to be true initially

Answer

It represents the hypothesis being tested

Answer

It represents the hypothesis that is rejected if the p-value is less than 0.05

Answer

It represents the hypothesis that is always true

Question 40

What is the primary purpose of a confidence interval?

Accepted Answer

To estimate the true population parameter

Answer

To test the hypothesis that the population parameter is equal to a specific value

Answer

To determine the sample size needed for a study

Answer

To predict future outcomes

Question 41

Which of the following variables is considered qualitative?

Accepted Answer

Gender

Answer

Age

Answer

Height

Answer

Income

Question 42

Which of the following is an example of a categorical variable?

Accepted Answer

Gender

Answer

Height

Answer

Age

Answer

Income

Question 43

Which of the following is a measure of variability?

Accepted Answer

Variance

Answer

Mean

Answer

Median

Answer

Mode

Question 44

Which of the following is NOT a type of sampling method?

Accepted Answer

Voluntary response sampling

Answer

Convenience sampling

Answer

Stratified sampling

Answer

Cluster sampling

Question 45

What is the key difference between a population and a sample?

Accepted Answer

A population is the entire group of individuals being studied, while a sample is a subset of that group.

Answer

A population is larger than a sample.

Answer

A sample is representative of a population.

Answer

A sample is used to make inferences about a population.

Question 46

What is the main purpose of using a confidence interval in statistics?

Accepted Answer

To estimate the population parameter with a range of possible values.

Answer

To test a statistical hypothesis.

Answer

To determine the sample size needed for a study.

Answer

To calculate the probability of a given event.

Question 47

Two balls are drawn at random, with replacement, from a bag containing 10 identical balls, numbered 1 to 10. What is the probability that the sum of the numbers on the balls is even?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Answer

1/5

Question 48

The correlation coefficient between two variables is -0.7. Does this indicate a strong or weak correlation?

Accepted Answer

Strong negative correlation

Answer

Strong positive correlation

Answer

Weak negative correlation

Answer

No correlation

Question 49

A hypothesis test is conducted using a significance level of 0.05. The p-value of the test is 0.06. What is the conclusion of the test?

Accepted Answer

Fail to reject the null hypothesis

Answer

Reject the null hypothesis

Answer

Insufficient evidence to conclude

Answer

The test is inconclusive

Question 50

Which of the following is NOT a type of probability distribution?

Accepted Answer

Trigonometric distribution

Answer

Normal distribution

Answer

Binomial distribution

Answer

Poisson distribution

Question 51

The correlation coefficient between two variables X and Y is -0.7. What does this indicate?

Accepted Answer

A strong negative correlation

Answer

A strong positive correlation

Answer

A weak negative correlation

Answer

A weak positive correlation

Question 52

A bag contains 5 red balls, 3 blue balls, and 2 green balls. If a ball is drawn at random, what is the probability of **not** drawing a blue ball?

Accepted Answer

7/10

Answer

1/2

Answer

2/5

Question 53

A survey of 200 students found that 120 students like mathematics. What is the sample proportion of students who **dislike** mathematics?

Accepted Answer

0.4

Answer

120

Answer

0.5

Answer

0.12

Question 54

The mean of a data set is 10 and the standard deviation is 2. What is the z-score for a value of 8?

Accepted Answer

-1

Answer

2

Answer

0.5

Answer

0

Question 55

Which of the following is a measure of **variability**?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 56

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

Accepted Answer

As one variable increases, the other tends to decrease.

Answer

As one variable decreases, the other tends to decrease as well.

Answer

There is no relationship between the two variables.

Question 57

A hypothesis test is conducted with a significance level of 0.05. The p-value is found to be 0.04. What is the conclusion of the test?

Accepted Answer

Reject the null hypothesis

Answer

Insufficient evidence to conclude

Answer

Type II error occurred

Answer

Fail to reject the null hypothesis

Question 58

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

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 59

A normal distribution has a mean of 50 and a standard deviation of 10. What is the probability of randomly selecting a value that is between 40 and 60?

Accepted Answer

0.6827

Answer

0.5000

Answer

0.3173

Answer

0.1587

Question 60

Which of the following is NOT a type of sampling method?

Accepted Answer

Regression analysis

Answer

Simple random sampling

Answer

Cluster sampling

Answer

Stratified sampling

Question 61

What is the null hypothesis in a hypothesis test?

Accepted Answer

There is no difference between the groups.

Answer

The median of the first group is less than the median of the second group.

Answer

There is a difference between the groups.

Answer

The mean of the first group is greater than the mean of the second group.

Question 62

What is the probability of rolling a 6 on a fair six-sided die?

Accepted Answer

1/6

Answer

1/5

Answer

1/3

Answer

1/4

Question 63

Which symbol represents the variance of a population?

Accepted Answer

σ²

Answer

s²

Answer

s

Answer

σ

Question 64

What is the mode of the data set: 2, 4, 6, 6, 8, 10?

Accepted Answer

6

Answer

10

Answer

4

Answer

8