Statistics for Year 12: Enhance Your Data Analysis Skills

Question 1

In a hypothesis test about the mean of a population, the null hypothesis proposes that the population mean is:

Accepted Answer

Equal to the hypothesized mean

Answer

Equal to the sample mean

Answer

Greater than or equal to the hypothesized mean

Answer

Less than or equal to the hypothesized mean

Question 2

Which of the following is NOT a measure of the strength of a linear relationship?

Accepted Answer

Mean of the residuals

Answer

Correlation coefficient

Answer

Coefficient of determination

Answer

Slope of the regression line

Question 3

What is the best description of the correlation coefficient?

Accepted Answer

A measure of the strength and direction of the linear relationship between two variables, ranging from -1 to 1.

Answer

A measure of the slope of the line of best fit.

Answer

A measure of the variability of the data.

Answer

Always a positive value.

Question 4

What is the essential condition for a linear correlation between two variables?

Accepted Answer

Data points forming a straight line on a scatterplot

Answer

Evenly spaced data points

Answer

Normally distributed data points

Answer

Strong positive correlation between data points

Question 5

In a linear relationship between two variables, which measure quantifies the strength and direction of the relationship?

Accepted Answer

Correlation coefficient

Answer

Mean

Answer

Standard deviation

Answer

Regression coefficient

Question 6

Which of the following is NOT a measure of the strength of a linear relationship between two variables?

Accepted Answer

Mean of the data

Answer

Correlation coefficient

Answer

Coefficient of determination (R squared)

Answer

Slope of the regression line

Question 7

To determine whether a correlation is statistically significant, which of these is used?

Accepted Answer

p-value

Answer

Correlation

Answer

Linear Regression

Answer

Coefficient of determination

Question 8

In hypothesis testing for a simple linear regression model, which approach is used to determine significance?

Accepted Answer

Calculate the p-value for the regression coefficient

Answer

Compare the correlation coefficient to a critical value

Answer

Compare the slope of the regression line to the slope of a line of best fit

Answer

Conduct a t-test on the residuals from the regression model

Question 9

Which of these is not a measure of central tendency?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 10

Which of the following statements about the correlation between two quantitative variables is incorrect?

Accepted Answer

The correlation between two variables can exceed 1.

Answer

A correlation of 0 indicates no linear relationship between the variables.

Answer

A strong positive correlation indicates a positive linear relationship between the variables.

Answer

A negative correlation indicates a negative linear relationship between the variables.

Question 11

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

Accepted Answer

Variance

Answer

Mean

Answer

Median

Answer

Mode

Question 12

Given two variables, X and Y, with a perfect negative linear relationship, what is the value of their correlation coefficient?

Accepted Answer

-1

Answer

0

Answer

1

Answer

2

Question 13

What statistical method is used to determine the strength and direction of a linear relationship between two variables?

Accepted Answer

Correlation

Answer

Linear regression

Answer

Analysis of variance

Question 14

Which of the following is a defining characteristic of the binomial distribution?

Accepted Answer

It models the number of successes in a series of independent Bernoulli trials.

Answer

It is a continuous probability distribution.

Answer

Its mean is always greater than its number of trials.

Answer

Its variance is always less than its mean.

Question 15

Which of the following statistics does NOT measure the strength of a linear relationship between two variables?

Accepted Answer

Standard deviation

Answer

Correlation coefficient

Answer

Coefficient of determination

Answer

Slope of the regression line

Question 16

Which statistical measure calculates the difference between the highest and lowest values in a dataset?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 17

When two variables have a strong positive linear relationship, what is the value of their correlation coefficient?

Accepted Answer

1

Answer

-1

Answer

0

Question 18

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

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 19

In linear regression, what does the slope of the regression line represent?

Accepted Answer

Rate of change in the dependent variable for each unit change in the independent variable

Answer

Average value of the independent variable

Answer

Strength of the relationship between the variables

Question 20

In a linear regression model, what does the slope of the line of best fit represent?

Accepted Answer

Change in the dependent variable for a unit change in the independent variable

Answer

Mean of the dataset

Answer

Standard deviation of the dataset

Answer

Correlation coefficient of the variables

Question 21

When a scatterplot displays a positive relationship between two variables, what can be inferred?

Accepted Answer

As one variable increases, the other variable also increases.

Answer

As one variable decreases, the other variable also decreases.

Answer

There is no relationship between the two variables.

Answer

The relationship between the two variables is non-linear.

Question 22

Differentiate between a population and a sample.

Accepted Answer

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

Answer

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

Answer

A population is a group with similar characteristics, while a sample is a group with different characteristics.

Answer

A sample is a group representative of the population, while a population is a group not representative of the sample.

Question 23

What is the primary purpose of statistical inference?

Accepted Answer

Drawing conclusions about a population based on a sample.

Answer

Collecting data from a population.

Answer

Analyzing data from a sample.

Answer

Predicting the future.

Question 24

In a hypothesis test, which statement represents the null hypothesis?

Accepted Answer

There is no significant difference between the two groups being compared.

Answer

The data supports the alternative hypothesis.

Answer

The null hypothesis is valid.

Answer

The sample mean is equal to the population mean.

Question 25

What is the term for the value that separates the rejection region from the non-rejection region in a hypothesis test?

Accepted Answer

Critical value

Answer

P-value

Answer

Level of significance

Answer

Sample mean

Question 26

Which type of regression analysis models the relationship between a dependent variable and one or more independent variables?

Accepted Answer

Linear regression

Answer

Logistic regression

Answer

Analysis of variance (ANOVA)

Answer

Chi-squared test

Question 27

In linear regression, the coefficient of determination (R-squared) represents:

Accepted Answer

The proportion of variation in the dependent variable explained by the independent variable(s).

Answer

The level of significance of the regression model.

Answer

The slope of the regression line.

Answer

The intercept of the regression line.

Question 28

What is the key difference between a one-tailed and a two-tailed hypothesis test?

Accepted Answer

A one-tailed test examines a specific direction of an effect, while a two-tailed test examines both directions of an effect.

Answer

A one-tailed test is more powerful than a two-tailed test.

Answer

A two-tailed test is more conservative than a one-tailed test.

Answer

There is no difference between the two types of hypothesis tests.

Question 29

What is the purpose of constructing a confidence interval?

Accepted Answer

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

Answer

To determine whether the null hypothesis is true or false.

Answer

To predict future observations.

Answer

To calculate the sample size needed for a hypothesis test.

Question 30

Differentiate between a Type I and a Type II error:

Accepted Answer

A Type I error occurs when the null hypothesis is rejected although it is true, while a Type II error occurs when the null hypothesis is not rejected although it is false.

Answer

A Type I error is more serious than a Type II error.

Answer

A Type II error is more serious than a Type I error.

Answer

There is no difference between a Type I and a Type II error.

Question 31

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

Accepted Answer

t-test

Answer

ANOVA

Answer

Chi-squared test

Answer

Correlation analysis

Question 32

In a linear regression model, the slope indicates:

Accepted Answer

The change in the dependent variable for each unit change in the independent variable.

Answer

The value of the dependent variable when the independent variable is zero.

Answer

The strength of the linear relationship between the two variables.

Answer

The probability that the dependent variable will increase as the independent variable increases.

Question 33

In a hypothesis test, the critical region is the area where:

Accepted Answer

The null hypothesis is rejected.

Answer

The null hypothesis is accepted.

Answer

The confidence interval is located.

Answer

The p-value is calculated.

Question 34

A researcher wants to compare the average test scores of students from two different schools. Which statistical method is most suitable?

Accepted Answer

ANOVA (Analysis of Variance)

Answer

Linear regression

Answer

Non-parametric test

Answer

Chi-squared test

Question 35

A company wants to compare the effectiveness of three training programs on employee performance. Which statistical method should they use to analyze the differences in performance between the groups?

Accepted Answer

ANOVA

Answer

T-test

Answer

Correlation analysis

Answer

Regression analysis

Question 36

In hypothesis testing, the step of calculating the p-value involves:

Accepted Answer

Comparing the test statistic to the critical value

Answer

Formulating the research question

Answer

Collecting and analyzing data

Answer

Determining the critical value

Question 37

A t-test is used to determine if:

Accepted Answer

The means of two independent samples are different

Answer

The correlation between two variables is significant

Answer

A regression model is statistically significant

Answer

The variance of a population is known

Question 38

Which of the following factors does NOT affect the power of a hypothesis test?

Accepted Answer

Population size

Answer

Sample size

Answer

Significance level

Answer

Effect size

Question 39

The primary distinction between a confidence interval and a significance test is that:

Accepted Answer

A confidence interval provides an estimate of a population parameter, while a significance test tests a hypothesis about a population parameter

Answer

A significance test provides an estimate of a population parameter, while a confidence interval tests a hypothesis about a population parameter

Answer

A confidence interval is always wider than a significance test

Answer

A confidence interval is always narrower than a significance test

Question 40

Which type of regression analysis involves modeling a binary outcome variable?

Accepted Answer

Logistic regression

Answer

Linear regression

Answer

Poisson regression

Answer

Multinomial regression

Question 41

The coefficient of determination (R-squared) in regression analysis represents:

Accepted Answer

The proportion of variance in the dependent variable explained by the independent variable(s)

Answer

The slope of the regression line

Answer

The intercept of the regression line

Answer

The standard error of the regression

Question 42

In a hypothesis test about the slope of a regression line, the null hypothesis typically states that:

Accepted Answer

The slope is equal to zero

Answer

The slope is not equal to zero

Answer

The slope is greater than zero

Answer

The slope is less than zero

Question 43

The key difference between a simple linear regression model and a multiple linear regression model is:

Accepted Answer

The number of independent variables included in the model

Answer

The type of relationship assumed between the variables

Answer

The accuracy of the model

Answer

The complexity of the model

Question 44

What is the primary purpose of a null hypothesis?

Accepted Answer

To state that there is no statistically significant difference or relationship between variables.

Answer

To state that there is a statistically significant difference or relationship between variables.

Answer

To prove that a hypothesis is true.

Question 45

In the context of a t-test, which of the following is a necessary condition for its validity?

Accepted Answer

The sample data is approximately normally distributed.

Answer

The population mean is known.

Answer

The sample size is very large.

Question 46

What is the main purpose of calculating a p-value?

Accepted Answer

To determine the level of statistical significance of the results and provide evidence against the null hypothesis.

Answer

To calculate the probability of making a correct decision.

Answer

To estimate the population parameters.

Question 47

Which of the following is NOT a type of regression analysis?

Accepted Answer

Chi-square test

Answer

Multiple regression

Answer

Logistic regression

Answer

Simple linear regression

Question 48

What does the slope of a regression line represent?

Accepted Answer

The change in the dependent variable for each unit change in the independent variable.

Answer

The correlation coefficient between the independent and dependent variables.

Answer

The y-intercept of the regression line.

Question 49

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

Accepted Answer

Correlation coefficient

Answer

Coefficient of determination

Answer

Standard error of the estimate

Answer

p-value

Question 50

What is the null hypothesis in a simple linear regression analysis?

Accepted Answer

There is no linear relationship between the independent variable and the dependent variable.

Answer

There is a positive linear relationship between the independent variable and the dependent variable.

Answer

There is a negative linear relationship between the independent variable and the dependent variable.

Question 51

Identify a limitation of regression analysis.

Accepted Answer

Regression models can only be used to predict linear relationships.

Answer

Regression models are always accurate.

Answer

Regression models require large sample sizes.

Question 52

A researcher wants to test whether a new teaching method improves students' test scores. He randomly assigns students to either the new method or the traditional method, and then gives them a test. The results are shown in the table below:

| Group | Mean Score | Standard Deviation |
|---|---|---|
| New Method | 75 | 10 |
| Traditional Method | 70 | 12 |

Which of the following hypotheses is being tested?

Accepted Answer

The mean score of the new method is higher than the mean score of the traditional method.

Answer

The standard deviation of the new method is lower than the standard deviation of the traditional method.

Answer

The mean score of the traditional method is higher than the mean score of the new method.

Question 53

What is the p-value of a hypothesis test?

Accepted Answer

The probability of obtaining a test statistic as extreme as or more extreme than the one observed, assuming the null hypothesis is true.

Answer

The probability of rejecting the null hypothesis.

Question 54

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 mean of one group is greater than the mean of the other group.

Question 55

What is the alternative hypothesis in a hypothesis test?

Accepted Answer

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

Answer

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

Answer

The hypothesis that the mean of one group is greater than the mean of the other group.

Question 56

What is a confidence interval?

Accepted Answer

A range of values that is likely to contain the true population parameter with a specified confidence level.

Answer

A hypothesis about the value of the true population parameter.

Answer

A single value that is the best estimate of the true population parameter.

Question 57

How is the width of a confidence interval determined?

Accepted Answer

By the level of confidence, the sample size, and the standard error of the mean.

Answer

By the p-value and the test statistic.

Answer

By the sample size and the standard deviation.

Question 58

What is the purpose of a regression analysis?

Accepted Answer

To determine the relationship between a dependent variable and one or more independent variables and make predictions.

Answer

To estimate the population mean of a variable.

Answer

To test whether there is a significant difference between two or more groups.

Question 59

What is the equation of a regression line?

Accepted Answer

y = mx + c

Answer

y = c

Answer

y = x + c

Answer

y = mx

Question 60

In a two-sample t-test, the null hypothesis states that:

Accepted Answer

The means of the two populations are equal.

Answer

The mean of population 1 is less than the mean of population 2.

Answer

The mean of population 1 is greater than the mean of population 2.

Question 61

Which of the following is an assumption of linear regression?

Accepted Answer

The residuals are normally distributed.

Answer

There are no outliers in the data.

Answer

The variance of the residuals is decreasing.

Answer

The relationship between the independent and dependent variables is non-linear.

Question 62

The correlation coefficient measures the:

Accepted Answer

Strength and direction of the linear relationship between two variables.

Answer

Difference between the actual data and the predicted values in linear regression.

Answer

Slope of the regression line in linear regression.

Question 63

What is the purpose of a residual plot in linear regression?

Accepted Answer

To check the assumption of normality and identify outliers.

Answer

To calculate the correlation coefficient.

Answer

To predict the value of the dependent variable for a given value of the independent variable.

Question 64

The expected value of a binomial distribution with parameters n and p is:

Accepted Answer

np

Answer

1-p

Answer

p(1-p)

Answer

n/p