Statistics Quizzes for Year 13 Mathematics | Sixth Form College

Question 1

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

Accepted Answer

1/6

Answer

1/5

Answer

1/4

Answer

1/3

Question 2

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

Accepted Answer

Rejecting the null hypothesis when it is true.

Answer

Accepting the null hypothesis when it is false.

Answer

Failing to reject the null hypothesis when it is false.

Answer

Rejecting the alternative hypothesis when it is true.

Question 3

In a scatterplot with a linear relationship, identify the formula to calculate the slope of the regression line.

Accepted Answer

Covariance of x and y variables / Variance of x variable

Answer

Mean of x-values / Mean of y-values

Answer

Standard deviation of x-values / Standard deviation of y-values

Answer

Correlation coefficient between x and y variables

Question 4

Which measure of central tendency describes the value that occurs most frequently in a dataset?

Accepted Answer

Mode

Answer

Mean

Answer

Median

Answer

Standard deviation

Question 5

Which of the following would be an appropriate null hypothesis for a study investigating the effectiveness of a new drug?

Accepted Answer

There is no difference in effectiveness between the new drug and the current standard treatment.

Answer

The new drug is less effective than the current standard treatment.

Answer

The new drug is more effective than the current standard treatment.

Answer

The new drug has a significant effect on the condition being treated.

Question 6

Which of the following is a type of statistical bias that occurs when participants respond differently based on how they are asked the question?

Accepted Answer

Response bias

Answer

Selection bias

Answer

Sampling bias

Answer

Observer bias

Question 7

A scatterplot shows a negative correlation between two variables. Which of the following statements is true?

Accepted Answer

As one variable increases, the other variable tends to decrease.

Answer

As one variable increases, the other variable also tends to increase.

Answer

The variables are positively correlated.

Answer

The scatterplot is not a reliable measure of the relationship between the variables.

Question 8

Data from 2000 to 2020 shows a positive correlation between the number of mobile subscriptions and the number of road accidents. Which of the following is a valid conclusion based on this finding?

Accepted Answer

The data alone cannot be used to establish a causal relationship between mobile subscriptions and road accidents.

Answer

An increase in mobile subscriptions directly causes an increase in road accidents.

Answer

A decrease in mobile subscriptions will lead to a decrease in road accidents.

Answer

There is no relationship between mobile subscriptions and road accidents.

Question 9

A normal distribution has a mean of 50 and a standard deviation of 10. What is the probability of randomly selecting a value less than 40 from this distribution?

Accepted Answer

0.0228

Answer

0.1587

Answer

0.3413

Answer

0.4772

Question 10

Which test statistic is used to test the hypothesis that two population means are equal?

Accepted Answer

t-test

Answer

Z-test

Answer

Chi-square test

Answer

F-test

Question 11

Which measure quantifies the strength and direction of a linear relationship between two variables?

Accepted Answer

Correlation coefficient

Answer

Regression coefficient

Answer

Slope

Answer

Intercept

Question 12

Which non-parametric statistical test is used to compare the medians of two independent samples?

Accepted Answer

Mann-Whitney U test

Answer

Wilcoxon signed-rank test

Answer

Kruskal-Wallis test

Answer

Friedman test

Question 13

A hypothesis test yields a p-value of 0.04. Considering a significance level of 0.05, which conclusion is appropriate?

Accepted Answer

Reject the null hypothesis.

Answer

Fail to reject the null hypothesis.

Answer

The hypothesis is true.

Answer

The hypothesis is false.

Question 14

Which of the following properties does NOT apply to a typical normal distribution?

Accepted Answer

Mean, median, and mode are identical

Answer

Bell-shaped curve

Answer

Symmetrical around the mean

Answer

Approximately 68% of data falls within one standard deviation of the mean

Question 15

What is the probability that an event will NOT occur if the probability of it occurring is 0.4?

Accepted Answer

0.6

Answer

0.4

Answer

0.8

Answer

1.0

Question 16

Which of the following is a non-parametric test? Non-parametric tests are statistical tests that do not assume that the data comes from a particular probability distribution.

Accepted Answer

Mann-Whitney U test

Answer

Chi-squared test

Answer

t-test

Answer

Linear regression

Question 17

What does a correlation coefficient of -0.9 indicate?

Accepted Answer

Strong negative relationship between variables

Answer

Strong positive relationship between variables

Answer

Moderate positive relationship between variables

Answer

Moderate negative relationship between variables

Question 18

What is the primary purpose of a confidence interval?

Accepted Answer

Estimating a population parameter

Answer

Testing a hypothesis

Answer

Predicting future events

Answer

Determining the significance of a difference

Question 19

A survey finds that 60% of respondents support a certain policy. What is the probability that a randomly selected respondent supports this policy?

Accepted Answer

0.6

Answer

0.4

Answer

0.3

Answer

0.2

Question 20

Which of the following is a measure of central tendency?

Accepted Answer

Mean

Answer

Interquartile range

Answer

Variance

Answer

Standard deviation

Question 21

Which of the following is the correct notation for the Poisson distribution?

Accepted Answer

Pois(λ)

Answer

Bin(n, p)

Answer

Norm(μ, σ)

Answer

Exp(λ)

Question 22

A hypothesis test is conducted at a 1% significance level. The p-value is found to be 0.02. What is the decision?

Accepted Answer

Reject the null hypothesis

Answer

Accept the alternative hypothesis

Answer

Fail to reject the null hypothesis

Answer

Fail to accept the alternative hypothesis

Question 23

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

Accepted Answer

Range

Answer

Mode

Answer

Median

Answer

Mean

Question 24

Which of the following is considered the best measure of variability?

Accepted Answer

Standard deviation

Answer

Interquartile range

Answer

Variance

Answer

Range

Question 25

A researcher wants to study the impact of sleep deprivation on academic performance. Which of the following research designs is most appropriate?

Accepted Answer

Controlled experiment

Answer

Case study

Answer

Cross-sectional study

Answer

Observational study

Question 26

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

Accepted Answer

Convenience

Answer

Stratified

Answer

Systematic

Answer

Cluster

Question 27

The probability of rolling an even number on a standard six-sided die is:

Accepted Answer

1/2

Answer

1/4

Answer

1/3

Answer

1/6

Question 28

A hypothesis test is conducted with a significance level of 0.01. The p-value of the test is 0.005. What is the conclusion of the test?

Accepted Answer

Reject the null hypothesis

Answer

The data is significant

Answer

The test is inconclusive

Answer

Fail to reject the null hypothesis

Question 29

A survey of 1000 students showed that 650 students use social media daily. What is the sample proportion of students who use social media daily?

Accepted Answer

0.65

Answer

0.35

Answer

0.75

Answer

1

Question 30

What is the purpose of a confidence interval?

Accepted Answer

To estimate a population parameter with a specified level of confidence

Answer

To test a hypothesis

Answer

To predict future values

Question 31

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

Accepted Answer

As one variable increases, the other variable tends to decrease

Answer

As one variable increases, the other variable tends to increase

Answer

There is no relationship between the two variables

Question 32

A fair six-sided die is rolled. What is the probability of rolling a number greater than 3?

Accepted Answer

1/2

Answer

1/4

Answer

1/6

Answer

1/3

Question 33

A sample of 100 students is taken from a population with a mean height of 170 cm and a standard deviation of 10 cm.  Assuming the heights are normally distributed, what is the probability that the sample mean height is between 168 cm and 172 cm?

Accepted Answer

0.6827

Answer

0.3173

Answer

0.0455

Answer

0.9545

Question 34

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

Accepted Answer

Range

Answer

Median

Answer

Mean

Answer

Mode

Question 35

A correlation coefficient of -0.8 indicates a strong:

Accepted Answer

Negative correlation

Answer

No correlation

Answer

Positive correlation

Answer

Weak correlation

Question 36

Which of the following is a non-parametric test?

Accepted Answer

Mann-Whitney U test

Answer

t-test

Answer

Regression analysis

Answer

ANOVA

Question 37

What is the 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 the population.

Answer

A population is a group of individuals who have a common characteristic, while a sample is a group of individuals who are not related.

Question 38

What is the primary purpose of a confidence interval?

Accepted Answer

To provide a range of values within which the true population parameter is likely to fall.

Answer

To test the significance of a hypothesis.

Answer

To provide a single value for the population parameter.