A random sample of 402 people were surveyed and each person was asked to report the highest education level they obtained. The data that resulted from the survey is summarized in the following table: High School Bachelors Masters Ph.D. Total Female 61 55 48 41 205 Male 42 44 53 58 197 Total 103 99 101 99 402 A) This sample has degree of freedom: ��= If gender and highest education level are independent, then B) With any expected count accurate to 2 decimal places, the expected count in row 1 column 3 is �1,3= C) With any component accurate to 2 decimal places, the component value in row 1 column 3 of the table is component1,3= D) �2 value of this sample is �2= . Round to 2 decimal places E) At significance level 0.02, is the sample showing strong evidence that gender and highest education level are dependent? Use 4 decimal places for p-value. Yes No F) The p-value of this sample was:
A random sample of 402 people were surveyed and each person was asked to report the highest education level they obtained. The data that resulted from the survey is summarized in the following table: High School Bachelors Masters Ph.D. Total Female 61 55 48 41 205 Male 42 44 53 58 197 Total 103 99 101 99 402 A) This sample has degree of freedom: ��= If gender and highest education level are independent, then B) With any expected count accurate to 2 decimal places, the expected count in row 1 column 3 is �1,3= C) With any component accurate to 2 decimal places, the component value in row 1 column 3 of the table is component1,3= D) �2 value of this sample is �2= . Round to 2 decimal places E) At significance level 0.02, is the sample showing strong evidence that gender and highest education level are dependent? Use 4 decimal places for p-value. Yes No F) The p-value of this sample was:
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
A random sample of 402 people were surveyed and each person was asked to report the highest education level they obtained. The data that resulted from the survey is summarized in the following table:
| High School | Bachelors | Masters | Ph.D. | Total | |
|---|---|---|---|---|---|
| Female | 61 | 55 | 48 | 41 | 205 |
| Male | 42 | 44 | 53 | 58 | 197 |
| Total | 103 | 99 | 101 | 99 | 402 |
A) This sample has degree of freedom:
��=
If gender and highest education level are independent, then
B) With any expected count accurate to 2 decimal places, the expected count in row 1 column 3 is
�1,3=
C) With any component accurate to 2 decimal places, the component value in row 1 column 3 of the table is
component1,3=
D) �2 value of this sample is
�2= . Round to 2 decimal places
E) At significance level 0.02, is the sample showing strong evidence that gender and highest education level are dependent? Use 4 decimal places for p-value.
- Yes
- No
F) The p-value of this sample was:
![### Chi-Square Test of Independence: Gender and Highest Education Level
A random sample of 402 people was surveyed, and each person was asked to report the highest education level they obtained. The data that resulted from the survey is summarized in the following table:
| Highest Education Level | High School | Bachelors | Masters | Ph.D. | Total |
|-------------------------|-------------|-----------|---------|-------|-------|
| **Female** | 61 | 55 | 48 | 41 | 205 |
| **Male** | 42 | 44 | 53 | 58 | 197 |
| **Total** | 103 | 99 | 101 | 99 | 402 |
#### Calculation Steps
A) **Degree of Freedom (DF)**:
\[ DF = \_\_\_\_\_\_ \]
B) **Expected Count**:
If gender and highest education level are independent, the expected count in row 1 column 3 can be denoted as \( E_{1,3} \).
\[ E_{1,3} = \_\_\_\_\_\_ \]
C) **Component Value**:
The component value in row 1 column 3 of the table is calculated with accuracy to 2 decimal places.
\[ \text{component}_{1,3} = \_\_\_\_\_\_ \]
D) **Chi-Square Value**:
The \(\chi^2\) value of this sample is calculated and rounded to 2 decimal places.
\[ \chi^2 = \_\_\_\_\_\_ \]
E) **Significance Test**:
At significance level 0.02, determine if the sample shows strong evidence that gender and highest education level are dependent. Use 4 decimal places for the \( p \)-value.
- Yes
- No
F) **P-Value**:
The \( p \)-value of this sample was:
\[ \text{p-value} = \_\_\_\_\_\_ \]
Please fill in the blanks with the appropriate values based on the chi-square test calculations. This will help in evaluating the dependence between gender and highest education level obtained.
### Explanation of Terms
- **Degree of Freedom (DF)**: This is calculated as \((\text{number of rows} -](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81fcbcae-c7c7-47f7-b9b9-962fae442be8%2F3ae1e1e6-1266-4c61-95da-3e1e2b72c413%2F23byjs_processed.png&w=3840&q=75)
Transcribed Image Text:### Chi-Square Test of Independence: Gender and Highest Education Level
A random sample of 402 people was surveyed, and each person was asked to report the highest education level they obtained. The data that resulted from the survey is summarized in the following table:
| Highest Education Level | High School | Bachelors | Masters | Ph.D. | Total |
|-------------------------|-------------|-----------|---------|-------|-------|
| **Female** | 61 | 55 | 48 | 41 | 205 |
| **Male** | 42 | 44 | 53 | 58 | 197 |
| **Total** | 103 | 99 | 101 | 99 | 402 |
#### Calculation Steps
A) **Degree of Freedom (DF)**:
\[ DF = \_\_\_\_\_\_ \]
B) **Expected Count**:
If gender and highest education level are independent, the expected count in row 1 column 3 can be denoted as \( E_{1,3} \).
\[ E_{1,3} = \_\_\_\_\_\_ \]
C) **Component Value**:
The component value in row 1 column 3 of the table is calculated with accuracy to 2 decimal places.
\[ \text{component}_{1,3} = \_\_\_\_\_\_ \]
D) **Chi-Square Value**:
The \(\chi^2\) value of this sample is calculated and rounded to 2 decimal places.
\[ \chi^2 = \_\_\_\_\_\_ \]
E) **Significance Test**:
At significance level 0.02, determine if the sample shows strong evidence that gender and highest education level are dependent. Use 4 decimal places for the \( p \)-value.
- Yes
- No
F) **P-Value**:
The \( p \)-value of this sample was:
\[ \text{p-value} = \_\_\_\_\_\_ \]
Please fill in the blanks with the appropriate values based on the chi-square test calculations. This will help in evaluating the dependence between gender and highest education level obtained.
### Explanation of Terms
- **Degree of Freedom (DF)**: This is calculated as \((\text{number of rows} -
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