15. Calculate x² for this sample data. a. 1.75 b. 2.17 c. 3.02 d. 4.76 Ans. 16. Instead of using your x² for number 14, let's say x²= 6.0. If the degrees of freedom is 2, what is the P-value for this problem? (If you use the table in the book, choose the value below that fits in the range you find). a. 0.287 b. 0.928 C. 0.050 d. 0.010 Ans. 17. Let's say you fail to reject the Null hypothesis for this problem. Choose the best conclusion. a. At a = 0.05, the data indicate that party and spending are independent. b. At a = 0.01, the data indicate that party and spending are not independent. c. At a = 0.01, the data indicate that party and spending are independent. At a = 0.05, the data indicate that party and spending are not independent. d.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
100%
Help me solve questions 15-17 using the following data
### Chi-Square Test for Independence of US Senators' Party Affiliation and Spending

#### Problems 12-17

The table below presents data on the number of US Senators from each political party based on their federal spending in three spending categories. The table is intended to aid in the calculation of the Chi-square test for independence, specifically at the 0.05 significance level. The table includes blanks that need to be filled to arrive at both row and column totals. 

You need to:
1. Record the total number of data points for each spending category and political party.
2. Perform a Chi-square test to determine whether there is a significant relationship between party affiliation and spending.

#### Table: Number of US Senators by Party and Spending Category

|                  | Less than 4 Billion | 4 to 7 Billion | More than 7 Billion | Totals |
|------------------|---------------------|----------------|----------------------|--------|
| **Democrat**     |          12         |       19       |          16          |   47   |
| **Republican**   |          8          |       15       |          22          |   45   |
| **Totals**       |          20         |       34       |          38          |   92   |

#### Explanation of the Table:
- The rows represent the party affiliation of the Senators (Democrat or Republican).
- The columns represent different categories of federal spending: Less than 4 Billion, 4 to 7 Billion, and More than 7 Billion.
- The last column provides the total number of Senators for each party.
- The last row provides the total number of Senators in each spending category.
- The bottom-right cell provides the overall total number of Senators included in the table (92).

This setup is integral for computing the expected frequencies and conducting the Chi-square test for the independence of party affiliation and federal spending habits. You will fill in any missing data points and compute the necessary statistical measures to draw a conclusion about the relationship between the variables.
Transcribed Image Text:### Chi-Square Test for Independence of US Senators' Party Affiliation and Spending #### Problems 12-17 The table below presents data on the number of US Senators from each political party based on their federal spending in three spending categories. The table is intended to aid in the calculation of the Chi-square test for independence, specifically at the 0.05 significance level. The table includes blanks that need to be filled to arrive at both row and column totals. You need to: 1. Record the total number of data points for each spending category and political party. 2. Perform a Chi-square test to determine whether there is a significant relationship between party affiliation and spending. #### Table: Number of US Senators by Party and Spending Category | | Less than 4 Billion | 4 to 7 Billion | More than 7 Billion | Totals | |------------------|---------------------|----------------|----------------------|--------| | **Democrat** | 12 | 19 | 16 | 47 | | **Republican** | 8 | 15 | 22 | 45 | | **Totals** | 20 | 34 | 38 | 92 | #### Explanation of the Table: - The rows represent the party affiliation of the Senators (Democrat or Republican). - The columns represent different categories of federal spending: Less than 4 Billion, 4 to 7 Billion, and More than 7 Billion. - The last column provides the total number of Senators for each party. - The last row provides the total number of Senators in each spending category. - The bottom-right cell provides the overall total number of Senators included in the table (92). This setup is integral for computing the expected frequencies and conducting the Chi-square test for the independence of party affiliation and federal spending habits. You will fill in any missing data points and compute the necessary statistical measures to draw a conclusion about the relationship between the variables.
### Statistical Analysis Exercises

---

#### Problems 18-22

**15. Calculate \(\chi^2\) for this sample data.**

- a. 1.75
- b. 2.17
- c. 3.02
- d. 4.76

**Ans.** _______

---

**16. Instead of using your \(\chi^2\) for number 14, let's say \(\chi^2\) = 6.0. If the degrees of freedom is 2, what is the p-value for this problem? (If you use the table in the book, choose the value below that fits in the range you find.)**

- a. 0.050
- b. 0.010
- c. 0.928
- d. 0.298

**Ans.** _______

---

**17. Let's say you fail to reject the Null hypothesis for this problem. Choose the best conclusion.**

- a. At \(\alpha\) = 0.05, the data indicate that property and spending are independent.
- b. At \(\alpha\) = 0.01, the data indicate that property and spending are independent.
- c. At \(\alpha\) = 0.01, the data indicate that property and spending are not independent.
- d. At \(\alpha\) = 0.05, the data indicate that property and spending are not independent.

**Ans.** _______

---

These exercises involve the application and interpretation of the Chi-square (\(\chi^2\)) statistic, p-values, and hypothesis testing. Review the relevant statistical concepts and techniques as needed to solve these problems.

*Note: There are no graphs or diagrams in the provided text.*
Transcribed Image Text:### Statistical Analysis Exercises --- #### Problems 18-22 **15. Calculate \(\chi^2\) for this sample data.** - a. 1.75 - b. 2.17 - c. 3.02 - d. 4.76 **Ans.** _______ --- **16. Instead of using your \(\chi^2\) for number 14, let's say \(\chi^2\) = 6.0. If the degrees of freedom is 2, what is the p-value for this problem? (If you use the table in the book, choose the value below that fits in the range you find.)** - a. 0.050 - b. 0.010 - c. 0.928 - d. 0.298 **Ans.** _______ --- **17. Let's say you fail to reject the Null hypothesis for this problem. Choose the best conclusion.** - a. At \(\alpha\) = 0.05, the data indicate that property and spending are independent. - b. At \(\alpha\) = 0.01, the data indicate that property and spending are independent. - c. At \(\alpha\) = 0.01, the data indicate that property and spending are not independent. - d. At \(\alpha\) = 0.05, the data indicate that property and spending are not independent. **Ans.** _______ --- These exercises involve the application and interpretation of the Chi-square (\(\chi^2\)) statistic, p-values, and hypothesis testing. Review the relevant statistical concepts and techniques as needed to solve these problems. *Note: There are no graphs or diagrams in the provided text.*
Expert Solution
steps

Step by step

Solved in 4 steps

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman