A professor using an open source introductory statistics book predicts that 15% of the students will purchase a hard copy of the book, 35% will print it out from the web, and 50% will read it online. At the end of the semester he asks his students to complete a survey where they indicate what format of the book they used. Of the 276 students, 36 said they bought a hard copy of the book, 107 said they printed it out from the web, and 133 said they read it online. Round all answers to four decimal places.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
A professor using an open source introductory statistics book predicts that 15% of the students will purchase a hard copy of the book, 35% will print it out from the web, and 50% will read it online. At the end of the semester he asks his students to complete a survey where they indicate what format of the book they used. Of the 276 students, 36 said they bought a hard copy of the book, 107 said they printed it out from the web, and 133 said they read it online. Round all answers to four decimal places.
![### Hypothesis Testing Exercise
#### 2. Enter the expected values for the hypothesis test in the table below:
| Book Format | Expected Value |
|----------------|----------------|
| Hard copy | |
| Print from web | |
| Read online | |
#### 3. Calculate the chi-squared statistic:
[Text box for answer]
#### 4. Calculate the degrees of freedom:
[Text box for answer]
#### 5. Calculate the p-value:
[Text box for answer]
---
#### Instructions:
1. **Expected Values**:
- In the table provided, enter the expected values for each book format based on your hypothesis.
2. **Chi-Squared Statistic**:
- Calculate the chi-squared statistic using the formula:
\[
\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}
\]
where \(O_i\) is the observed frequency and \(E_i\) is the expected frequency.
3. **Degrees of Freedom**:
- Calculate the degrees of freedom for your test using the formula:
\[
\text{Degrees of Freedom} = (r - 1)(c - 1)
\]
where \(r\) is the number of rows and \(c\) is the number of columns.
4. **P-Value**:
- Use the chi-squared statistic and degrees of freedom to find the p-value from the chi-squared distribution table or using statistical software.
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This exercise will help you understand how to perform hypothesis testing using the chi-squared test for independence. Ensure your calculations are accurate and review the statistical methods if needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8585c01c-e95f-4e9e-ab09-9be83264bdef%2F7c64df43-1700-44f9-ab1f-06b66a7bcccb%2F4t4pf0f_processed.png&w=3840&q=75)
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