Your friend Micah helped you with the null and alternative hypotheses... Ho : The proportions are consistent with the national report. H₁: At least one of the proportion is different from the national report. Outcome Never Married 231 Married Widowed Observed Frequency Divorced 389 49 106 The degree of freedom = The test-statistic for this data The p-value for this sample = Expected Frequency (Round to 3 decimal places) (Please show your answer to three decimal places.) (Please show your answer to four decimal places.)
Your friend Micah helped you with the null and alternative hypotheses... Ho : The proportions are consistent with the national report. H₁: At least one of the proportion is different from the national report. Outcome Never Married 231 Married Widowed Observed Frequency Divorced 389 49 106 The degree of freedom = The test-statistic for this data The p-value for this sample = Expected Frequency (Round to 3 decimal places) (Please show your answer to three decimal places.) (Please show your answer to four decimal places.)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 26E
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Question
A recent national report states the marital status distribution of the male population age 18 or older is as follows: Never Married (32%), Married (54.1%), Widowed (2.3%), Divorced (11.6%). The table below shows the results of a random sample of 775 adult men from California. Test the claim that the claim that the marital status distribution of the male population age 18 or older is different from the recent national report at the significant level of a = 0.1.
![### Chi-Square Test for Independence
To determine whether the observed frequencies of marital status categories in your data set are consistent with the national report, we will conduct a chi-square test for independence using the following hypotheses:
**Null Hypothesis (** \(H_0\) **)**: The proportions are consistent with the national report.
**Alternative Hypothesis (** \(H_1\) **)**: At least one of the proportions is different from the national report.
Complete the table with the expected frequencies (rounded to three decimal places) calculated based on the national report:
| Outcome | Observed Frequency | Expected Frequency (Round to 3 decimal places) |
| ------------- | ------------------- | ----------------------------------------------- |
| Never Married | 231 | |
| Married | 389 | |
| Widowed | 49 | |
| Divorced | 106 | |
### Steps to Complete the Analysis:
1. **Calculate the Expected Frequencies**:
- For each category (Never Married, Married, Widowed, Divorced), compute the expected frequencies based on national proportions.
2. **Fill in the Expected Frequencies** in the table provided.
3. **Calculate the Chi-Square Test Statistic**:
- The formula for the chi-square test statistic \( χ^2 \) is:
\[
χ^2 = \sum \frac{(O_i - E_i)^2}{E_i}
\]
Where \(O_i\) is the observed frequency, and \(E_i\) is the expected frequency.
Provide your test statistic (to three decimal places):
\[
\text{The test-statistic for this data = } \_\_\_\_\_\_
\]
4. **Determine the Degrees of Freedom**:
- The degrees of freedom (\( df \)) for this test is calculated as:
\[
df = (\text{number of categories} - 1)
\]
Provide the degree of freedom:
\[
\text{The degree of freedom = } \_\_\_\_\_
\]
5. **Find the p-value**:
- Based on the chi-square test statistic and the degrees of freedom, find the p-value from chi-square distribution tables or using statistical software.
Provide your p-value (to four decimal places):
\[
\text{The p-value for](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3268b88a-f4fb-4fae-897e-35b47f1612ff%2F3cdd7066-5ba0-44f4-b11d-29d87f964750%2Fog0x0kw_processed.png&w=3840&q=75)
Transcribed Image Text:### Chi-Square Test for Independence
To determine whether the observed frequencies of marital status categories in your data set are consistent with the national report, we will conduct a chi-square test for independence using the following hypotheses:
**Null Hypothesis (** \(H_0\) **)**: The proportions are consistent with the national report.
**Alternative Hypothesis (** \(H_1\) **)**: At least one of the proportions is different from the national report.
Complete the table with the expected frequencies (rounded to three decimal places) calculated based on the national report:
| Outcome | Observed Frequency | Expected Frequency (Round to 3 decimal places) |
| ------------- | ------------------- | ----------------------------------------------- |
| Never Married | 231 | |
| Married | 389 | |
| Widowed | 49 | |
| Divorced | 106 | |
### Steps to Complete the Analysis:
1. **Calculate the Expected Frequencies**:
- For each category (Never Married, Married, Widowed, Divorced), compute the expected frequencies based on national proportions.
2. **Fill in the Expected Frequencies** in the table provided.
3. **Calculate the Chi-Square Test Statistic**:
- The formula for the chi-square test statistic \( χ^2 \) is:
\[
χ^2 = \sum \frac{(O_i - E_i)^2}{E_i}
\]
Where \(O_i\) is the observed frequency, and \(E_i\) is the expected frequency.
Provide your test statistic (to three decimal places):
\[
\text{The test-statistic for this data = } \_\_\_\_\_\_
\]
4. **Determine the Degrees of Freedom**:
- The degrees of freedom (\( df \)) for this test is calculated as:
\[
df = (\text{number of categories} - 1)
\]
Provide the degree of freedom:
\[
\text{The degree of freedom = } \_\_\_\_\_
\]
5. **Find the p-value**:
- Based on the chi-square test statistic and the degrees of freedom, find the p-value from chi-square distribution tables or using statistical software.
Provide your p-value (to four decimal places):
\[
\text{The p-value for
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