You are conducting a test of homogeneity for the claim that two different populations have the same proportions of the following two characteristics. Here is the sample data. Category A B A B Population Population # 1 #2 The expected observations for this table would be Category Population Population # 1 #2 A 10 B 46 22 92 The resulting Pearson residuals are: Category Population Population #1 #2 What is the chi-square test-statistic for this data? x² =
You are conducting a test of homogeneity for the claim that two different populations have the same proportions of the following two characteristics. Here is the sample data. Category A B A B Population Population # 1 #2 The expected observations for this table would be Category Population Population # 1 #2 A 10 B 46 22 92 The resulting Pearson residuals are: Category Population Population #1 #2 What is the chi-square test-statistic for this data? x² =
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Hi, I' not sure how to find Pearson residuals. Thank you!
![### Conducting a Test of Homogeneity
**Objective**: You are conducting a test of homogeneity for the claim that two different populations have the same proportions of the following two characteristics. Here is the sample data:
#### Sample Data
| Category | Population #1 | Population #2 |
|----------|---------------|---------------|
| A | 10 | 22 |
| B | 46 | 92 |
#### Expected Observations
The expected observations for this table would be:
| Category | Population #1 | Population #2 |
|----------|---------------|---------------|
| A | | |
| B | | |
#### Pearson Residuals
The resulting Pearson residuals are:
| Category | Population #1 | Population #2 |
|----------|---------------|---------------|
| A | | |
| B | | |
#### Chi-Square Test-Statistic
What is the chi-square test-statistic for this data?
\[ \chi^2 = \]
To fill out this table, you will need to calculate the expected counts and the Pearson residuals based on the data given. The chi-square test-statistic can be calculated 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.
This test helps to determine whether there is a significant difference between the expected and observed frequencies in one or more categories.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3268b88a-f4fb-4fae-897e-35b47f1612ff%2Fc75e8d88-fc3e-4bbe-a050-4b619a5a842e%2Fkg23xg_processed.png&w=3840&q=75)
Transcribed Image Text:### Conducting a Test of Homogeneity
**Objective**: You are conducting a test of homogeneity for the claim that two different populations have the same proportions of the following two characteristics. Here is the sample data:
#### Sample Data
| Category | Population #1 | Population #2 |
|----------|---------------|---------------|
| A | 10 | 22 |
| B | 46 | 92 |
#### Expected Observations
The expected observations for this table would be:
| Category | Population #1 | Population #2 |
|----------|---------------|---------------|
| A | | |
| B | | |
#### Pearson Residuals
The resulting Pearson residuals are:
| Category | Population #1 | Population #2 |
|----------|---------------|---------------|
| A | | |
| B | | |
#### Chi-Square Test-Statistic
What is the chi-square test-statistic for this data?
\[ \chi^2 = \]
To fill out this table, you will need to calculate the expected counts and the Pearson residuals based on the data given. The chi-square test-statistic can be calculated 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.
This test helps to determine whether there is a significant difference between the expected and observed frequencies in one or more categories.
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