Statistics Quizzes for Year 12 Mathematics: Master Statistical Concepts

Question 1

Which of these is a measure of dispersion, not a measure of central tendency?

Accepted Answer

Variance

Answer

Mean

Answer

Median

Answer

Mode

Question 2

Which of the following hypotheses is the alternative hypothesis?

Accepted Answer

H1: μ > 50

Answer

H0: μ = 50

Answer

H0: μ ≠ 50

Answer

H1: μ < 50

Question 3

A sample of 100 students has a mean height of 170 cm and a standard deviation of 5 cm. What is the 95% confidence interval for the population mean height?

Accepted Answer

(168.8, 171.2)

Answer

(169.5, 170.5)

Answer

(167.9, 172.1)

Answer

(172.1, 177.9)

Question 4

A data set has a positive skewness. What does this indicate?

Accepted Answer

The data is more spread out on the right side.

Answer

The data is more spread out on the left side.

Answer

The mean is less than the median.

Answer

The median is less than the mode.

Question 5

Which of the following is a qualitative variable?

Accepted Answer

Gender

Answer

Age

Answer

Income

Answer

Height

Question 6

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

Accepted Answer

Mode

Answer

Mean

Answer

Median

Answer

Range

Question 7

Identify the statistical test used to compare the means of two independent samples:

Accepted Answer

t-test

Answer

ANOVA

Answer

Chi-square test

Answer

Correlation coefficient

Question 8

A study is conducted to determine the relationship between height and weight. The correlation coefficient is 0.8. What does this value indicate?

Accepted Answer

A strong positive correlation

Answer

A strong negative correlation

Answer

A weak positive correlation

Answer

A weak negative correlation

Question 9

What is the purpose of a confidence interval?

Accepted Answer

To estimate the population parameter

Answer

To test a hypothesis

Answer

To predict future values

Answer

To describe the shape of a distribution

Question 10

Which of the following is a measure of dispersion?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 11

What is a key distinction between parametric and non-parametric tests?

Accepted Answer

Parametric tests assume a normal distribution, while non-parametric tests do not.

Answer

Parametric tests are more powerful than non-parametric tests.

Question 12

Which of the following probability distributions is used to model the number of successes in a sequence of independent experiments with a constant probability of success?

Accepted Answer

Binomial distribution

Answer

Normal distribution

Answer

Poisson distribution

Answer

Exponential distribution

Question 13

A 95% confidence interval is an interval that contains the true population mean with:

Accepted Answer

95% probability

Answer

99% probability

Answer

90% probability

Answer

80% probability

Question 14

The correlation coefficient between two variables measures:

Accepted Answer

The strength and direction of the linear relationship between two variables

Answer

The strength and direction of the non-linear relationship between two variables

Answer

The probability that one variable will cause the other variable to change

Answer

The average value of the two variables

Question 15

Which of the following is a use of regression analysis?

Accepted Answer

Predicting the value of one variable based on the value of another variable

Answer

Determining if there is a significant relationship between two variables

Answer

Testing the significance of the difference between two means

Answer

Estimating the population mean

Question 16

In a hypothesis test, what does a p-value of 0.05 suggest?

Accepted Answer

The probability of rejecting the null hypothesis when it is true is 0.05.

Answer

The probability of the null hypothesis being true is 0.05.

Answer

The probability of accepting the alternative hypothesis is 0.05.

Answer

The p-value measures the effect size.

Question 17

Which of these is a measure of central tendency?

Accepted Answer

Mean

Answer

Range

Answer

Variance

Answer

Correlation coefficient

Question 18

A hypothesis test is conducted to determine if the average height of a certain population is different from 170 cm. The null hypothesis is:

Accepted Answer

H0: μ = 170 cm

Answer

H0: μ > 170 cm

Answer

H0: μ < 170 cm

Answer

H0: μ ≠ 170 cm

Question 19

A scatter plot shows a moderate negative correlation between two variables. Which of the following conclusions can be drawn from this?

Accepted Answer

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

Answer

As one variable decreases, the other variable tends to increase.

Answer

There is no relationship between the two variables.

Answer

The relationship between the two variables is non-linear.

Question 20

In constructing a confidence interval, how does increasing the sample size affect the margin of error?

Accepted Answer

Decreases

Answer

Increases

Answer

No change

Question 21

Which measure of central tendency is most susceptible to the influence of outliers?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 22

Which of the following is an example of a non-parametric test?

Accepted Answer

Mann-Whitney U test

Answer

t-test

Answer

ANOVA

Question 23

A scatterplot shows a strong negative correlation between two variables. Which of the following is a possible interpretation of this relationship?

Accepted Answer

As the value of one variable increases, the value of the other variable decreases.

Answer

As the value of one variable decreases, the value of the other variable increases.

Answer

There is no relationship between the two variables.

Question 24

Which of the following is a type of systematic error?

Accepted Answer

Measurement error

Answer

Sampling error

Answer

Non-response error

Question 25

In a hypothesis test with a significance level of 5%, what is the critical value for a two-tailed test assuming a normal distribution?

Accepted Answer

1.96

Answer

2.576

Answer

1.645

Answer

1.282

Question 26

A survey asks participants to rate their agreement with a statement on a scale from strongly disagree to strongly agree. What type of data is this?

Accepted Answer

Ordinal data

Answer

Nominal data

Answer

Interval data

Answer

Ratio data

Question 27

Which measure of dispersion is most heavily influenced by extreme values, such as outliers?

Accepted Answer

Range

Answer

Interquartile range

Answer

Standard deviation

Answer

Variance

Question 28

A scatterplot reveals a strong positive correlation between two variables. What does this suggest?

Accepted Answer

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

Answer

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

Answer

The variables are not related to each other.

Answer

The relationship between the variables is nonlinear.

Question 29

When flipping a fair coin, what is the probability of getting tails?

Accepted Answer

0.5

Answer

0.25

Answer

0.75

Answer

1

Question 30

Which of the following is not a measure of central tendency used to describe the average of a dataset?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 31

The range of a dataset is defined as the difference between its maximum and minimum values. If a dataset has a range of 30, what is the gap between the highest and lowest values in that dataset?

Accepted Answer

30

Answer

10

Answer

15

Answer

60

Question 32

In a fair coin toss experiment, the probability of getting heads or tails on any given toss is 50%. If a coin is tossed 10 times, what is the probability of obtaining exactly 5 heads?

Accepted Answer

0.24

Answer

0.10

Answer

0.49

Answer

0.98

Question 33

In sampling techniques, which type of sampling involves selecting every nth individual from a population, where n is a fixed interval?

Accepted Answer

Systematic sampling

Answer

Simple random sampling

Answer

Stratified sampling

Answer

Convenience sampling

Question 34

What is the median of the following dataset: 4, 6, 2, 8, 10?

Accepted Answer

6

Answer

4

Answer

5

Answer

7

Question 35

If the standard deviation of a dataset is zero, what does this imply about the data?

Accepted Answer

All values in the dataset are identical

Answer

The data is evenly distributed around the mean

Answer

The data is skewed to the right

Answer

The data is skewed to the left

Question 36

A sample of 100 students has an average age of 18 years. If a new student with an age of 22 years joins the group, what will be the updated average age of the sample?

Accepted Answer

18.04

Answer

18.02

Answer

18.06

Answer

18.08

Question 37

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

Accepted Answer

Standard Deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 38

What is the null hypothesis in a hypothesis test?

Accepted Answer

The hypothesis that there is no significant difference between the groups being compared.

Answer

The hypothesis that there is a significant difference between the groups being compared.

Answer

The hypothesis that the sample is representative of the population.

Answer

The hypothesis that the data is normally distributed.

Question 39

Which of the following is a sampling method that gives every member of the population an equal chance of being selected?

Accepted Answer

Simple random sampling

Answer

Systematic sampling

Answer

Stratified sampling

Answer

Cluster sampling

Question 40

Calculate the standard deviation of the following data set: {1, 3, 5, 7, 9}.

Accepted Answer

2.83 (rounded to two decimal places)

Answer

1.5

Answer

3.5

Answer

4.2

Question 41

Which of the following probability distributions represents outcomes that can take on any value within a specific range?

Accepted Answer

Normal distribution

Answer

Hypergeometric distribution

Answer

Poisson distribution

Answer

Binomial distribution

Question 42

In the context of hypothesis testing, which hypothesis is initially assumed to be true until proven otherwise?

Accepted Answer

The null hypothesis

Answer

The research hypothesis

Answer

The alternative hypothesis

Question 43

Which of the following is a method used to select a sample from a population?

Accepted Answer

Stratified sampling

Answer

Correlation

Answer

Mean

Answer

Regression

Question 44

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

Accepted Answer

A population refers to the entire group of individuals being studied, while a sample is a subset of that population chosen to represent the whole.

Answer

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

Question 45

Which statistical measure quantifies the asymmetry of a distribution?

Accepted Answer

Pearson's coefficient of skewness

Answer

Variance

Answer

Standard deviation

Question 46

What is the fundamental difference between a discrete and a continuous variable?

Accepted Answer

A discrete variable can only take on specific, distinct values, while a continuous variable can take on any value within a given range.

Answer

A continuous variable can only take on specific, distinct values, while a discrete variable can take on any value within a given range.

Question 47

Which of the following is a graphical representation commonly used to display the distribution of a data set?

Accepted Answer

Histogram

Answer

Mean

Answer

Correlation

Answer

Standard deviation

Question 48

What is the primary purpose of constructing a confidence interval?

Accepted Answer

To estimate the true population parameter within a specified margin of error and confidence level.

Answer

To test the null hypothesis

Answer

To calculate the p-value

Question 49

A dataset contains the following values: 5, 7, 7, 8, 8, 8, 9, 10. What is the most frequently occurring value in this dataset, known as the?

Accepted Answer

Mode: 8

Answer

Range: 5

Answer

Mean: 7.5

Answer

Median: 8

Question 50

The variance of a dataset is 9. What is the positive square root of the variance, known as the?

Accepted Answer

Standard deviation: 3

Answer

Range: 6

Answer

Interquartile range: 3

Answer

Mean: 9

Question 51

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability of drawing a red ball?

Accepted Answer

5/8

Answer

1/2

Answer

3/5

Answer

3/8

Question 52

Which of the following statements about a normal distribution is not true?

Accepted Answer

It is skewed to the left or right.

Answer

It is bell-shaped and symmetrical.

Answer

The mean, median, and mode are equal.

Question 53

In a hypothesis test, the null hypothesis states that there is no difference between two population means. The p-value is calculated to be 0.02. Based on a significance level of 0.05, what can be concluded?

Accepted Answer

Reject the null hypothesis

Answer

The p-value is not statistically significant

Answer

Accept the null hypothesis

Question 54

Which of the following is an example of discrete data?

Accepted Answer

The number of students in a class

Answer

The height of a tree

Answer

The weight of a package

Answer

The temperature of a room

Question 55

A study found a strong positive correlation between ice cream sales and crime rates. What can be concluded from this information?

Accepted Answer

Correlation does not imply causation, and other factors may be involved

Answer

Eating ice cream causes people to commit crimes

Answer

High crime rates lead to increased ice cream sales

Question 56

A researcher wants to estimate the average income of doctors in a city but cannot survey the entire population. Instead, a sample is used to collect data. What is the average income calculated from the sample an example of?

Accepted Answer

A statistic

Answer

A hypothesis

Answer

A parameter

Answer

A variable

Question 57

A box plot is used to visualize the distribution of a dataset. Which of the following can be determined from a box plot?

Accepted Answer

The median, quartiles, and range of the data

Answer

The mean and standard deviation of the data

Answer

The correlation coefficient between two variables

Answer

The exact values of all data points