10 Introduction to Inferential Statistics

Question 1

What is the main focus of the chapter?

Answer 1

The chapter focuses on data analysis, specifically t-tests, chi-square, correlations, and simple linear regression analyses

Includes hands-on practice to reinforce understanding.

Question 2

What are the three main types of t-tests?

Answer 2

• Independent t-test
• Dependent t-test
• One-sample t-test

Question 3

What does an independent t-test compare?

Answer 3

Two groups that are independent of each other

Samples include different people or observations.

Question 4

What is a dependent t-test?

Answer 4

A t-test that compares two groups that are inherently related

Example: collecting data from the same group at two different times.

Question 5

What does a one-sample t-test compare?

Answer 5

One group against a single value

Example: comparing class test scores against the mean of all test scores.

Question 6

What does a t-test generate that is used to determine statistical significance?

Answer 6

A t-score

Typically, the p-value is provided as a result by analytics tools.

Question 7

What are the key assumptions for an independent t-test?

Answer 7

• Independence
• Normality
• Homogeneity of variance
• n ≥ 30
• The independent variable is categorical
• The dependent variable is numerical

Question 8

What is the assumption of normality in a t-test?

Answer 8

The data is normally distributed.

Question 9

What does homogeneity of variance mean in the context of a t-test?

Answer 9

The variance of both groups is approximately the same.

Question 10

What is the significance of having at least 30 observations in each sample for a t-test?

Answer 10

It generally leads to better results.

Question 11

What is the independent variable in a t-test?

Answer 11

The variable that is controlled or changed, separating the two groups.

Question 12

What is the dependent variable in a t-test?

Answer 12

A numerical variable being compared between the two groups.

Question 13

What is a chi-square goodness of fit test used for?

Answer 13

To compare a sample to a population to see if the sample is a good representation.

Question 14

What does a chi-square test for independence compare?

Answer 14

Two categorical variables to see whether there is a relationship between them.

Question 15

What is the null hypothesis in a chi-square test for independence?

Answer 15

There is no relation between the two variables.

Question 16

What are the assumptions for a chi-square test for independence?

Answer 16

• Both variables are categorical
• Independence of observations

Question 17

What is a contingency table?

Answer 17

A frequency table that looks at more than one variable.

Question 18

What programming environment is used for running the t-test in this chapter?

Answer 18

Jupyter Notebooks

Question 19

What Python library is commonly used for statistical tests like t-tests?

Answer 19

SciPy

Question 20

Fill in the blank: A t-test compares two groups that contain _______.

Answer 20

[quantitative data]

Question 21

True or False: You need to perform a t-test for the exam.

Answer 21

False

You need to know the definition and application of a t-test.

Question 22

What is the purpose of running a t-test on Yorkshire Terriers and Singapura weights?

Answer 22

To determine if there is a significant difference in weight between the two breeds.

Question 23

What does the p-value indicate in a t-test result?

Answer 23

The statistical significance of the results.

Question 24

What is the mean weight of Singapura cats according to the example?

Answer 24

6.1 lb

Question 25

What is the mean weight of Yorkshire Terriers according to the example?

Answer 25

5.5 lb

Question 26

What is the difference in mean weight between Singapura cats and Yorkshire Terriers?

Answer 26

0.6 lb

Question 27

What is the main takeaway from performing t-tests according to the chapter?

Answer 27

Understanding how to differentiate t-tests from other analyses.

Question 28

What is the next analysis covered after t-tests in this chapter?

Answer 28

Chi-square analysis.

Question 29

What does a chi-square test for independence compare?

Answer 29

It compares two categorical variables by analyzing a contingency table.

Question 30

Define a contingency table.

Answer 30

A contingency table is another name for a frequency table that looks at more than one variable.

Question 31

List the assumptions of a chi-square test.

Answer 31

* Both variables are categorical * Independence of observations * Contingency cell exclusivity * 80% of cells should have a value of at least 5 * n ≥ 50

Question 32

What is meant by 'independence of observations' in a chi-square test?

Answer 32

Each observation needs to be independent of every other observation.

Question 33

Explain contingency cell exclusivity.

Answer 33

Each observation is only counted once in the contingency table.

Question 34

What is the minimum requirement for cell values in a chi-square test?

Answer 34

80% of the cells should have a count of 5 or more.

Question 35

What is the minimum sample size recommended for a chi-square test?

Answer 35

n ≥ 50.

Question 36

How do you calculate the number of cells in a contingency table?

Answer 36

Multiply the number of possible outcomes of one variable by the number of possible outcomes of the second variable.

Question 37

What does the p-value represent in a chi-square test?

Answer 37

It indicates whether there is a statistically significant relationship between the variables.

Question 38

What conclusion is drawn if the p-value is larger than 0.05 in a chi-square test?

Answer 38

Accept the null hypothesis and reject the alternative hypothesis.

Question 39

Define correlation in statistical terms.

Answer 39

A correlation is a relationship between two variables that can be positive or negative.

Question 40

What does a positive correlation indicate?

Answer 40

As one variable increases, so does the other.

Question 41

What does a negative correlation indicate?

Answer 41

As one variable increases, the other variable decreases.

Question 42

What does it mean when there is no correlation between two variables?

Answer 42

What happens to one variable has no impact on the other.

Question 43

True or False: Correlation implies causation.

Answer 43

False.

Question 44

What is the correlation coefficient?

Answer 44

A number that indicates the strength of the relationship between two variables, ranging from -1 to 1.

Question 45

What is the significance of the correlation coefficient being close to 1 or -1?

Answer 45

The closer the coefficient is to 1 or -1, the stronger the relationship.

Question 46

What type of analysis tests the strength of the relationship between two numerical variables?

Answer 46

Correlation analysis.

Question 47

List the assumptions for Pearson’s correlation analysis.

Answer 47

* Level of measurement * Linearity * Normality * Related pairs * Lack of outliers * n ≥ 30 * Two continuous variables

Question 48

What is simple linear regression primarily used for?

Answer 48

Prediction of one variable based on another.

Question 49

In simple linear regression, what does the x-axis represent?

Answer 49

The independent variable (predictor variable).

Question 50

In simple linear regression, what does the y-axis represent?

Answer 50

The dependent variable (criterion variable).

Question 51

What does the R² value indicate in regression analysis?

Answer 51

It tells how much variance in the dependent variable is explained by the independent variable.

Question 52

What is the null hypothesis in regression analysis?

Answer 52

The independent variable is NOT a predictor of the dependent variable.

Question 53

What is the alternative hypothesis in regression analysis?

Answer 53

The independent variable IS a predictor of the dependent variable.

Question 54

What is the minimum sample size recommended for correlation analysis?

Answer 54

n ≥ 30.

Question 55

What statistical method is used to determine if the number of nuts fed to squirrels can predict their weight?

Answer 55

Simple linear regression ## Footnote The p-value from the regression analysis was 0.043, indicating a statistically significant prediction.

Question 56

What is the p-value threshold commonly used to determine statistical significance in regression analysis?

Answer 56

0.05 ## Footnote A p-value below this threshold suggests that the independent variable can predict the dependent variable.

Question 57

In simple linear regression, which variable is considered the independent variable when predicting height?

Answer 57

Weight ## Footnote Height is the dependent variable in this context.

Question 58

What are the assumptions of simple linear regression? List them.

Answer 58

* Linearity * Normality * Independence * Homoscedasticity * The dependent variable is numeric * The independent variable is numeric * n % 100 ## Footnote Each assumption must be checked to ensure valid results.

Question 59

What does the term 'homoscedasticity' refer to in regression analysis?

Answer 59

The variance in the residuals remaining constant for different levels of the independent variable ## Footnote It means that the residuals are evenly spread around the regression line.

Question 60

What is the minimum sample size recommended for simple linear regression?

Answer 60

10 observations ## Footnote However, best practice suggests using at least 100 observations.

Question 61

What does the R-squared value represent in regression analysis?

Answer 61

The proportion of variance in the dependent variable explained by the independent variable ## Footnote An R-squared value of 0.92 means that 92% of the variance in height can be explained by weight.

Question 62

What function is used in Python to create a simple linear regression model?

Answer 62

sm.OLS() ## Footnote This function is part of the statsmodels library in Python.

Question 63

Fill in the blank: If you want to see whether there is a statistically significant difference between two groups using numeric variables, you would use a _______.

Answer 63

T-test

Question 64

Which analysis would be appropriate to determine if there is a relationship between two categorical variables?

Answer 64

Chi-square test ## Footnote This test is used for independence between two categorical variables.

Question 65

True or False: Correlation can be used to see whether two numeric variables are related and how strongly they are related.

Answer 65

True

Question 66

What is the appropriate analysis to predict one numeric variable using another numeric variable?

Answer 66

Simple linear regression