Inferential Statistics Quizzes: Test Your Understanding

Question 1

Which of the following is NOT a technique used in inferential statistics?

Accepted Answer

Descriptive statistics

Answer

Hypothesis testing

Answer

Confidence intervals

Answer

Regression analysis

Question 2

The p-value obtained from a hypothesis test represents the probability of:

Accepted Answer

Rejecting the null hypothesis when it is true.

Answer

Accepting the alternative hypothesis when it is true.

Answer

Accepting the null hypothesis when it is true.

Answer

Rejecting the alternative hypothesis when it is false.

Question 3

In hypothesis testing, the null hypothesis is typically stated as:

Accepted Answer

There is no significant difference or relationship.

Answer

There is a significant difference or relationship.

Answer

The sample is representative of the population.

Answer

The sample is not representative of the population.

Question 4

Which of the following is NOT a key assumption of linear regression?

Accepted Answer

Absence of outliers.

Answer

Linearity between the dependent and independent variables.

Answer

Independence of observations.

Answer

Homogeneity of variances.

Question 5

Which of the following is NOT a type of inferential statistic?

Accepted Answer

Descriptive statistics

Answer

Hypothesis testing

Answer

Confidence intervals

Answer

Regression analysis

Question 6

What does the term 'regression' refer to in the context of inferential statistics?

Accepted Answer

Predicting a continuous outcome variable based on one or more other variables

Answer

Testing a hypothesis about a population mean

Answer

Estimating a population proportion

Answer

Analyzing categorical data

Question 7

A regression equation is y = 5 + 2x. What does the slope of this equation represent?

Accepted Answer

The average change in y for a one-unit change in x

Answer

The y-intercept of the equation

Answer

The correlation coefficient between x and y

Answer

The error term in the regression model

Question 8

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

Accepted Answer

Fail to reject the null hypothesis

Answer

Reject the null hypothesis

Answer

The test is inconclusive

Answer

The p-value is too high to make a conclusion

Question 9

What is the distinction between a population and a sample in statistics?

Accepted Answer

A population is the entire set of individuals under investigation, while a sample is a subset of that population.

Answer

A sample is the entire set of individuals under investigation, while a population is a subset of that sample.

Answer

A population is a theoretical concept, while a sample is a real-world collection of data.

Answer

There is no difference between a population and a sample.

Question 10

What is the main objective of regression analysis in statistics?

Accepted Answer

To predict the value of a dependent variable based on the values of one or more independent variables.

Answer

To determine whether there is a statistically significant relationship between two or more variables.

Answer

To estimate the mean value of a population.

Answer

To describe the distribution of a variable.

Question 11

What does the coefficient of determination represent in regression analysis?

Accepted Answer

The proportion of variance in the dependent variable that is explained by the independent variables.

Answer

The strength of the relationship between the dependent variable and the independent variables.

Answer

The significance of the regression model.

Answer

The error in the regression model.

Question 12

What is the distinction between a Type I error and a Type II error in statistical hypothesis testing?

Accepted Answer

A Type I error occurs when we reject the null hypothesis when it is true, while a Type II error occurs when we fail to reject the null hypothesis when it is false.

Answer

A Type II error occurs when we reject the null hypothesis when it is true, while a Type I error occurs when we fail to reject the null hypothesis when it is false.

Answer

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

Answer

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

Question 13

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

Accepted Answer

Correlation coefficient

Answer

Regression line

Answer

Scatterplot

Answer

ANOVA

Question 14

A regression model with an R-squared value of 0.75 indicates that what percentage of variation in the dependent variable is explained by the independent variable?

Accepted Answer

75%

Answer

25%

Answer

50%

Answer

100%

Question 15

Which measure quantifies the variability in the residuals of a regression model?

Accepted Answer

Residual standard error

Answer

Correlation coefficient

Answer

Coefficient of determination

Answer

Adjusted R-squared

Question 16

What's the null hypothesis?

Accepted Answer

The hypothesis that the researcher assumes is true until proven otherwise.

Answer

The hypothesis that the researcher is testing.

Answer

The hypothesis that the researcher is trying to prove.

Answer

The hypothesis that the researcher rejects if the p-value is less than 0.05.

Question 17

How does the size of a sample impact the width of a confidence interval?

Accepted Answer

Smaller sample sizes result in wider confidence intervals.

Answer

Larger sample sizes result in wider confidence intervals.

Answer

The sample size has no effect on the width of a confidence interval.

Question 18

Which of the following is a measure used to quantify the strength and direction of the linear relationship between two variables?

Accepted Answer

Correlation coefficient

Answer

Standard error of the estimate

Answer

Regression coefficient

Answer

Coefficient of determination

Question 19

Which of the following is **not** a type of inferential statistic?

Accepted Answer

Descriptive statistics

Answer

Regression analysis

Answer

Hypothesis testing

Answer

Confidence intervals

Question 20

In hypothesis testing, what is the null hypothesis?

Accepted Answer

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

Answer

The hypothesis that the sample statistic is equal to the population parameter.

Answer

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

Question 21

What is a confidence interval?

Accepted Answer

A range of values that is likely to contain the true population mean.

Answer

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

Answer

A hypothesis that is tested using a sample.

Question 22

What is regression analysis used for?

Accepted Answer

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

Answer

Testing the difference between two groups.

Question 23

What are the assumptions of linear regression?

Accepted Answer

Linearity, independence, normality, and homoscedasticity.

Answer

Linearity, independence, heteroscedasticity, and normality.

Answer

Linearity, dependence, normality, and homoscedasticity.

Question 24

A researcher wants to test if the average height of students in a school is different from 1.75 meters. They collect data from a sample of 100 students. What type of hypothesis test should they use?

Accepted Answer

One-sample t-test

Answer

Two-sample t-test

Answer

Chi-squared test

Answer

Paired t-test

Question 25

A 95% confidence interval for the mean weight of a certain type of fruit is (100 grams, 120 grams). Which of the following statements is TRUE?

Accepted Answer

We are 95% confident that the true mean weight of the fruit lies between 100 grams and 120 grams.

Answer

There is a 95% chance that the next fruit we weigh will be between 100 grams and 120 grams.

Answer

95% of all fruit weigh between 100 grams and 120 grams.

Question 26

A study investigates the relationship between the number of hours spent studying and exam scores. The correlation coefficient is found to be 0.8. What does this indicate?

Accepted Answer

There is a strong positive linear relationship between hours spent studying and exam scores.

Answer

There is no relationship between hours spent studying and exam scores.

Answer

Hours spent studying causes higher exam scores.

Question 27

A researcher wants to test if there is a significant difference in the mean number of hours of sleep between students who use social media before bed and those who do not. Which type of hypothesis test should they use?

Accepted Answer

Two-sample t-test

Answer

One-sample t-test

Answer

Paired t-test

Answer

Chi-squared test

Question 28

What is the purpose of a p-value in hypothesis testing?

Accepted Answer

To determine the probability of observing the sample data, or more extreme data, assuming the null hypothesis is true.

Answer

To determine the probability of rejecting the null hypothesis.

Question 29

A regression analysis was performed to investigate the relationship between the number of hours spent exercising per week and body mass index (BMI). The regression equation is BMI = 25 - 0.5 * (Hours Exercising). What does the intercept of 25 represent?

Accepted Answer

The average BMI of people who do not exercise.

Answer

The maximum possible BMI.

Answer

The number of hours of exercise needed to maintain a BMI of 25.

Question 30

A researcher wants to estimate the proportion of students in a university who own a laptop. They randomly select 500 students and find that 400 own a laptop. Calculate the 99% confidence interval for the population proportion.

Accepted Answer

0.764 to 0.836

Answer

0.750 to 0.850

Answer

0.700 to 0.900

Answer

0.784 to 0.816

Question 31

Which of the following is a characteristic of a well-formulated hypothesis?

Accepted Answer

It is testable.

Answer

It is based on personal opinions and beliefs.

Answer

It is vague and ambiguous.

Answer

It is always proven to be true.

Question 32

A study investigates the relationship between the amount of time spent on social media and mental health. The scatterplot shows no clear pattern. Which of the following is a reasonable conclusion?

Accepted Answer

There is no significant relationship between the amount of time spent on social media and mental health.

Answer

Spending more time on social media improves mental health.

Answer

The study's results are inconclusive.

Question 33

A company wants to test if a new marketing campaign has increased sales. They compare sales figures before and after the campaign. Which type of hypothesis test should they use?

Accepted Answer

Paired t-test

Answer

One-sample t-test

Answer

Chi-squared test

Answer

Two-sample t-test

Question 34

A researcher wants to determine if a new teaching method improves student test scores. They randomly assign students to two groups: one receiving the new method and the other the traditional method.  What type of hypothesis test is most appropriate?

Accepted Answer

Two-sample t-test

Answer

One-sample t-test

Answer

Chi-squared test

Answer

Paired t-test

Question 35

A 95% confidence interval for the average height of women in a country is (160 cm, 165 cm). Which statement is TRUE about this interval?

Accepted Answer

We are 95% confident that the true average height of women in the country lies between 160 cm and 165 cm.

Answer

95% of women in the country have heights between 160 cm and 165 cm.

Question 36

A study investigates the relationship between hours of study and exam scores. The correlation coefficient is found to be 0.8. What can we conclude?

Accepted Answer

There is a strong positive linear association between hours of study and exam scores.

Answer

Hours of study directly cause higher exam scores.

Answer

There is no relationship between hours of study and exam scores.

Question 37

A researcher wants to test the hypothesis that the average IQ of students in a particular school is 100. What are the null and alternative hypotheses?

Accepted Answer

Null:  μ = 100, Alternative: μ ≠ 100

Answer

Null:  μ > 100, Alternative: μ ≤ 100

Answer

Null:  μ < 100, Alternative: μ ≥ 100

Answer

Null:  μ ≠ 100, Alternative: μ = 100

Question 38

A 99% confidence interval for the average age of students in a college is (18.5 years, 20.3 years). Which statement is FALSE?

Accepted Answer

We can be 99% certain that the average age of all college students is 19.4 years.

Answer

We are 99% confident that the true average age of college students lies between 18.5 years and 20.3 years.

Answer

The interval was calculated from a sample of college students.

Question 39

A study finds a correlation coefficient of -0.7 between the number of hours spent watching TV and the number of books read per week. What does this indicate?

Accepted Answer

There is a strong negative linear association between TV watching and book reading.

Answer

Watching more TV causes people to read fewer books.

Answer

There is no relationship between TV watching and book reading.

Question 40

A researcher wants to see if there is a difference in the proportion of students who pass a test after using two different study methods. What type of hypothesis test is appropriate?

Accepted Answer

Two-sample proportion test

Answer

Paired t-test

Answer

One-sample proportion test

Answer

Chi-squared test

Question 41

A 90% confidence interval for the average price of a certain type of car is (£15,000, £18,000). What is the margin of error?

Accepted Answer

£1,500

Answer

We cannot determine the margin of error from the given information.

Answer

£3,000

Answer

£16,500

Question 42

In a regression analysis, the coefficient of determination (R-squared) is 0.64. What does this mean?

Accepted Answer

64% of the variation in the dependent variable is explained by the independent variable.

Answer

The regression line predicts 64% of the data points correctly.

Answer

The correlation coefficient is 0.8.

Question 43

A researcher conducts a study to see if a new medication reduces blood pressure.  They find a p-value of 0.03.  What can be concluded?

Accepted Answer

There is strong evidence to suggest that the medication reduces blood pressure.

Answer

There is no evidence to suggest that the medication reduces blood pressure.

Answer

The medication definitely reduces blood pressure.