statistical inference

Question 1

What is statistical inference?

Answer 1

The process of drawing conclusions about a population based on a sample.

Question 2

True or False: Statistical inference can only be performed with large sample sizes.

Answer 2

False.

Question 3

Fill in the blank: A _______ is a numerical summary of a sample.

Answer 3

statistic

Question 4

What is a population in statistical terms?

Answer 4

The entire group of individuals or instances about whom we hope to learn.

Question 5

What is a sample?

Answer 5

A subset of the population selected for analysis.

Question 6

Multiple Choice: Which of the following is a common method for selecting a sample?

Answer 6

Random sampling.

Question 7

What is the purpose of hypothesis testing?

Answer 7

To determine whether there is enough evidence to reject a null hypothesis.

Question 8

True or False: The null hypothesis typically represents a statement of no effect or no difference.

Answer 8

True.

Question 9

Fill in the blank: The _______ is the probability of making a Type I error.

Answer 9

alpha level

Question 10

What is a Type I error?

Answer 10

Rejecting the null hypothesis when it is actually true.

Question 11

What is a Type II error?

Answer 11

Failing to reject the null hypothesis when it is false.

Question 12

Multiple Choice: Which of the following is a common significance level used in hypothesis testing?

Answer 12

0.05.

Question 13

What does p-value represent?

Answer 13

The probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true.

Question 14

True or False: A smaller p-value indicates stronger evidence against the null hypothesis.

Answer 14

True.

Question 15

What is confidence interval?

Answer 15

A range of values derived from a sample that is likely to contain the value of an unknown population parameter.

Question 16

Fill in the blank: A 95% confidence interval means that if we were to take many samples, _______ of those intervals would contain the true population parameter.

Answer 16

95%

Question 17

What is the Central Limit Theorem?

Answer 17

The theorem stating that the distribution of sample means approaches a normal distribution as the sample size increases.

Question 18

True or False: The Central Limit Theorem applies only to normally distributed populations.

Answer 18

False.

Question 19

What is a point estimate?

Answer 19

A single value estimate of a population parameter.

Question 20

Multiple Choice: Which of the following is NOT a method of estimation?

Answer 20

Extrapolation.

Question 21

What is the difference between descriptive statistics and inferential statistics?

Answer 21

Descriptive statistics summarize data, while inferential statistics draw conclusions about a population based on sample data.

Question 22

Fill in the blank: A _______ is a graphical representation of the distribution of a dataset.

Answer 22

histogram

Question 23

What is the purpose of a t-test?

Answer 23

To determine if there is a significant difference between the means of two groups.

Question 24

True or False: The t-test can only be used for normally distributed data.

Answer 24

False.

Question 25

What is ANOVA?

Answer 25

Analysis of Variance, a method used to compare means among three or more groups.

Question 26

Multiple Choice: Which of the following is a prerequisite for conducting ANOVA?

Answer 26

Independence of observations.

Question 27

What is a chi-square test used for?

Answer 27

To determine if there is a significant association between categorical variables.

Question 28

Fill in the blank: The _______ test is used to compare observed frequencies with expected frequencies.

Answer 28

chi-square

Question 29

True or False: Correlation implies causation.

Answer 29

False.

Question 30

What does a correlation coefficient of 1 indicate?

Answer 30

A perfect positive linear relationship between two variables.

Question 31

What does a correlation coefficient of -1 indicate?

Answer 31

A perfect negative linear relationship between two variables.

Question 32

Multiple Choice: What is the range of values for a correlation coefficient?

Answer 32

-1 to 1.

Question 33

What is regression analysis used for?

Answer 33

To model the relationship between a dependent variable and one or more independent variables.

Question 34

Fill in the blank: In regression analysis, the _______ variable is the one being predicted.

Answer 34

dependent

Question 35

True or False: In linear regression, the relationship between variables is assumed to be linear.

Answer 35

True.

Question 36

What is multicollinearity?

Answer 36

A situation in regression analysis where independent variables are highly correlated.

Question 37

What is the purpose of the residual analysis in regression?

Answer 37

To check the validity of the regression model by analyzing the differences between observed and predicted values.

Question 38

Multiple Choice: Which of the following is a common criterion for model selection in regression?

Answer 38

Adjusted R-squared.

Question 39

What is the difference between parametric and non-parametric tests?

Answer 39

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

Question 40

Fill in the blank: Non-parametric tests are often used when data does not meet _______ assumptions.

Answer 40

normality

Question 41

What is the role of sample size in statistical inference?

Answer 41

Larger sample sizes generally provide more reliable estimates and reduce sampling error.

Question 42

True or False: Increasing the sample size can decrease the margin of error.

Answer 42

True.

Question 43

What is the importance of random sampling?

Answer 43

It helps ensure that the sample is representative of the population, reducing bias.

Question 44

Multiple Choice: Which of the following is a common misconception about statistical significance?

Answer 44

Statistical significance implies practical significance.

Question 45

What is a power analysis?

Answer 45

A method used to determine the sample size required to detect an effect of a given size with a certain degree of confidence.

Question 46

Fill in the blank: The _______ is the probability of correctly rejecting the null hypothesis.

Answer 46

power

Question 47

What is effect size?

Answer 47

A quantitative measure of the magnitude of a phenomenon.

Question 48

True or False: Effect size can help to interpret the practical significance of a result.

Answer 48

True.

Question 49

What does the term 'sampling distribution' refer to?

Answer 49

The probability distribution of a statistic obtained from a large number of samples drawn from a specific population.

Question 50

Multiple Choice: Which of the following is a key assumption of linear regression?

Answer 50

Linearity of relationships.

Question 51

What is the significance of the F-test in ANOVA?

Answer 51

It tests whether there are significant differences between group means.

Question 52

Fill in the blank: The _______ is a summary measure that describes the strength and direction of a linear relationship between two variables.

Answer 52

correlation coefficient

Question 53

What is a confidence level?

Answer 53

The percentage of times that a confidence interval would contain the true population parameter if the same sampling method were repeated.

Question 54

True or False: A 99% confidence interval is wider than a 95% confidence interval.

Answer 54

True.