Statistics for Year 13: Master the Fundamentals of Data Analysis

Question 1

Which of the following is NOT a probability sampling technique?

Accepted Answer

Convenience sampling

Answer

Simple random sampling

Answer

Systematic sampling

Answer

Stratified sampling

Question 2

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

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 3

Which of the following sampling methods does NOT involve randomly selecting participants?

Accepted Answer

Convenience sampling

Answer

Simple random sampling

Answer

Stratified sampling

Answer

Cluster sampling

Question 4

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

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 5

Which of the following is a measure of dispersion?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 6

Which of the following is exclusively a measure of data spread?

Accepted Answer

Range

Answer

Mean

Answer

Median

Question 7

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

Accepted Answer

Quartiles

Answer

Mean

Answer

Median

Answer

Mode

Question 8

Which of the following measurements indicates the spread of data around its central value?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 9

Which of the following is an example of a continuous probability distribution?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Chi-square distribution

Question 10

A hypothesis test aims to determine if there is a statistically significant difference between two or more groups.

Accepted Answer

True

Answer

False

Question 11

Regression analysis is used to determine the relationship between a dependent variable and one or more independent variables.

Accepted Answer

True

Answer

False

Question 12

The line of best fit in a scatterplot is the line that minimizes the sum of the squared distances between the data points and the line.

Accepted Answer

True

Answer

False

Question 13

The coefficient of determination (R-squared) indicates the proportion of variance in the dependent variable that is explained by the independent variable(s).

Accepted Answer

True

Answer

False

Question 14

Examples of statistical fallacies include the gambler's fallacy and the bandwagon effect.

Accepted Answer

True

Answer

False

Question 15

Statistics can provide valuable insights and information to aid decision-making processes.

Accepted Answer

True

Answer

False

Question 16

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

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 17

In a hypothesis test, we aim to determine if the mean weight of a population differs from 100 kg. The null and alternative hypotheses are:

Accepted Answer

H0: μ = 100 kg, Ha: μ ≠ 100 kg

Answer

H0: μ ≠ 100 kg, Ha: μ = 100 kg

Answer

H0: μ < 100 kg, Ha: μ > 100 kg

Answer

H0: μ > 100 kg, Ha: μ < 100 kg

Question 18

Which type of residual plot do we use to assess the linearity of a regression model?

Accepted Answer

Residual versus fitted plot

Answer

Scatter plot

Answer

Normal probability plot

Answer

QQ plot

Question 19

A regression model has an R-squared value of 0.8. What percentage of variation in the dependent variable is explained by the independent variable?

Accepted Answer

80%

Answer

20%

Answer

50%

Answer

100%

Question 20

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

Accepted Answer

There is a strong negative relationship between the variables.

Answer

There is a strong positive relationship between the variables.

Answer

There is a moderate positive relationship between the variables.

Answer

There is no relationship between the variables.

Question 21

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

Accepted Answer

Variance

Answer

Mean

Answer

Median

Answer

Mode

Question 22

Which of the following is a continuous random variable?

Accepted Answer

The height of a person

Answer

The number of siblings a person has

Answer

The gender of a person

Answer

The number of days in a year

Question 23

Which of the following is a valid conclusion based on a hypothesis test with a p-value of 0.05?

Accepted Answer

Reject the null hypothesis

Answer

Fail to reject the null hypothesis

Answer

Accept the alternative hypothesis

Answer

Reject the alternative hypothesis

Question 24

The correlation coefficient between two variables is 0.85. What does this value indicate?

Accepted Answer

A strong positive correlation

Answer

A weak negative correlation

Answer

A strong negative correlation

Answer

A weak positive correlation

Question 25

Which of the following regression models is appropriate for predicting a continuous dependent variable using multiple independent variables?

Accepted Answer

Multiple regression

Answer

Logistic regression

Answer

Linear regression

Answer

Poisson regression

Question 26

The adjusted R-squared value for a regression model is 0.65. This indicates that:

Accepted Answer

65% of the variation in the dependent variable is explained by the independent variables

Answer

65% of the variation in the independent variables is explained by the dependent variable

Answer

35% of the variation in the dependent variable is explained by the independent variables

Answer

35% of the variation in the independent variables is explained by the dependent variable

Question 27

A linear regression model has an R-squared value of 0.85. What does this indicate?

Accepted Answer

The model explains 85% of the variation in the dependent variable.

Answer

The model explains 15% of the variation in the dependent variable.

Answer

The model has a strong positive correlation between the independent and dependent variables.

Answer

The model is not statistically significant.

Question 28

What is the difference between a population and a sample?

Accepted Answer

A population is the entire group of interest, while a sample is a smaller group that represents the population.

Answer

A sample is the entire group of interest, while a population is a smaller group that represents the sample.

Answer

A population and a sample are the same thing.

Answer

A sample is a random selection of individuals, while a population is a non-random selection of individuals.

Question 29

Which of the following is an example of a discrete probability distribution?

Accepted Answer

Binomial distribution

Answer

Uniform distribution

Answer

Normal distribution

Answer

Exponential distribution

Question 30

What is the most frequently occurring value in the following dataset: 5, 7, 9, 7, 11, 7, 13?

Accepted Answer

7

Answer

5

Answer

9

Answer

11

Question 31

Which of the following is a non-parametric statistical test?

Accepted Answer

Chi-squared test

Answer

t-test

Answer

ANOVA

Answer

Regression analysis

Question 32

What is the purpose of a confidence interval?

Accepted Answer

To estimate the population parameter with a specified level of confidence.

Answer

To test whether a particular value is equal to the population parameter.

Answer

To predict the value of future observations.

Answer

To determine the exact value of the population parameter.

Question 33

A variable with only two possible outcomes is known as a(n) variable:

Accepted Answer

Binary variable

Answer

Quantitative variable

Answer

Qualitative variable

Answer

Continuous variable

Question 34

What is the likelihood of an event that is certain?

Accepted Answer

1

Answer

0

Answer

0.5

Answer

0.25

Question 35

The mean of a data set represents:

Accepted Answer

The sum of all values divided by the number of values

Answer

The middle value of the data set

Answer

The value that occurs most frequently in the data set

Answer

The difference between the highest and lowest values in the data set

Question 36

Which measure quantifies the variability of a data set?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 37

In hypothesis testing, the null hypothesis states that:

Accepted Answer

There is no significant difference between the groups being compared

Answer

There is a significant difference between the groups being compared

Answer

The difference between the groups is equal to a specific value

Answer

The difference between the groups is greater than a specific value

Question 38

The primary purpose of a regression line is to:

Accepted Answer

Predict a dependent variable based on an independent variable

Answer

Determine the correlation between two variables

Answer

Describe the distribution of a data set

Answer

Generate random numbers

Question 39

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

Accepted Answer

t-test

Answer

ANOVA

Answer

Regression Analysis

Answer

Chi-square test

Question 40

Which of the following is a measure of the average value of a dataset?

Accepted Answer

Mean

Answer

Variance

Answer

Standard deviation

Answer

Correlation coefficient

Question 41

Which type of distribution is symmetrical and has a single peak?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Uniform distribution

Question 42

What is the statement that we are testing in a hypothesis test?

Accepted Answer

The null hypothesis

Answer

The alternative hypothesis

Answer

The research hypothesis

Answer

The statistical hypothesis

Question 43

What is the range of possible values for a correlation coefficient?

Accepted Answer

-1 to 1

Answer

0 to 1

Answer

-1 to 0

Answer

0 to 0.5

Question 44

What is the purpose of a confidence interval?

Accepted Answer

To estimate the true value of a parameter with a specified level of confidence

Answer

To test a hypothesis about the population mean

Answer

To predict future values of a variable

Answer

To determine the significance of a difference between two groups

Question 45

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

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 46

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

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 47

For a hypothesis test to be valid, which assumption is crucial?

Accepted Answer

Samples are independent and randomly selected.

Answer

Samples are randomly selected.

Answer

Population is normally distributed.

Question 48

In a hypothesis test, if the p-value is lower than the significance level, what should you conclude?

Accepted Answer

Reject the null hypothesis.

Answer

Reject the alternative hypothesis.

Answer

Increase the sample size.

Answer

Fail to reject the null hypothesis.

Question 49

Which of the following is NOT a measure of central tendency used to describe the 'typical value' of a dataset?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 50

Which sampling technique ensures that every individual in the population has an equal probability of being selected, thus minimizing bias?

Accepted Answer

Simple random sampling

Answer

Systematic sampling

Answer

Stratified sampling

Answer

Cluster sampling

Question 51

Which of the following is a measure of central tendency used to describe the 'average' of a distribution?

Accepted Answer

Mean

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 52

Which of the following is NOT a measure of central tendency, which provide summary information about the middle of the data set?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 53

In hypothesis testing, what is the probability of incorrectly rejecting a true null hypothesis? This probability is known as:

Accepted Answer

Type I error

Answer

Type II error

Answer

Statistical significance

Answer

Confidence interval

Question 54

Summarize the Central Limit Theorem.

Accepted Answer

As sample size increases, the distribution of sample means approaches a normal distribution.

Answer

The mean of a sample will always equal the population mean.

Answer

The variance of a sample will always equal the population variance.

Answer

The standard deviation of a sample will always equal the population standard deviation.

Question 55

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

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 56

The probability of rolling a 6 on a standard six-sided die is:

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 57

Which of the following is a continuous probability distribution?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Hypergeometric distribution

Question 58

In a hypothesis test, the null hypothesis is typically rejected if the p-value is:

Accepted Answer

Less than 0.05

Answer

Greater than 0.05

Answer

Greater than 0.10

Answer

Equal to 0.05

Question 59

The coefficient of determination (R-squared) measures the:

Accepted Answer

Strength but not direction of the relationship between two variables

Answer

Strength and direction of the relationship between two variables

Answer

Direction but not strength of the relationship between two variables

Answer

Neither the strength nor the direction of the relationship between two variables

Question 60

Corrected: Which probability distribution is symmetrical around its mean?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Exponential distribution

Question 61

Corrected: What is the purpose of a confidence interval?

Accepted Answer

To estimate a population parameter with a specified level of confidence

Answer

To test the significance of a difference between two means

Answer

To determine the sample size for a statistical study

Answer

To predict the outcome of a future event

Question 62

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

Accepted Answer

Independent samples t-test

Answer

Paired samples t-test

Answer

Analysis of variance (ANOVA)

Answer

Chi-square test

Question 63

Corrected: What is the most commonly used level of significance in statistical hypothesis testing?

Accepted Answer

0.05

Answer

0.01

Answer

0.10

Answer

0.20

Question 64

Which of the following is a measure of central tendency, representing the typical value of a dataset?

Accepted Answer

Mean

Answer

Variance

Answer

Standard deviation

Answer

Interquartile range