A biologist uses the chi-square test to determine whether the observed distribution of 5
species matches an expected theoretical distribution. The chi-square test yields a test
statistic of 9.488 .
What is the null hypothesis?
Select
What is the alternative hypothesis?
Select
What is the number of degrees of freedom? Ex- 5
What is the p-value? Ex 1.23 .
Does the data differ from expected distribution at the significance level?
Select

Ask by Wood Martinez. in the United States

Dec 17,2024

Question

A biologist uses the chi-square test to determine whether the observed distribution of 5
species matches an expected theoretical distribution. The chi-square test yields a test
statistic of 9.488 .
What is the null hypothesis?
Select
What is the alternative hypothesis?
Select
What is the number of degrees of freedom? Ex- 5
What is the p-value? Ex 1.23 .
Does the data differ from expected distribution at the significance level?
Select

Ask by Wood Martinez. in the United States

Dec 17,2024

UpStudy AI · Accepted Answer

To answer your questions regarding the chi-square test, let's break it down step by step.

### Null Hypothesis (H0)
The null hypothesis typically states that there is no significant difference between the observed and expected distributions. In this case, it can be formulated as:
- **H0**: The observed distribution of the 5 species matches the expected theoretical distribution.

### Alternative Hypothesis (H1)
The alternative hypothesis states that there is a significant difference between the observed and expected distributions. It can be formulated as:
- **H1**: The observed distribution of the 5 species does not match the expected theoretical distribution.

### Degrees of Freedom
The degrees of freedom (df) for a chi-square test is calculated as:
$$ \text{df} = k - 1 $$
where $$ k $$ is the number of categories (or species, in this case). Since there are 5 species:
$$ \text{df} = 5 - 1 = 4 $$

### P-value
To find the p-value associated with the chi-square test statistic of 9.488 and 4 degrees of freedom, you would typically refer to a chi-square distribution table or use statistical software.

Using a chi-square distribution calculator or table:
- For $$ \chi^{2} = 9.488 $$ with $$ df = 4 $$, the p-value is approximately **0.05**.

### Significance Level
To determine if the data differs from the expected distribution at the $$ \alpha = 0.01 $$ significance level, we compare the p-value to the significance level:
- Since $$ p \approx 0.05 $$ is greater than $$ \alpha = 0.01 $$, we **fail to reject the null hypothesis**.

### Summary of Answers
1. **Null Hypothesis (H0)**: The observed distribution of the 5 species matches the expected theoretical distribution.
2. **Alternative Hypothesis (H1)**: The observed distribution of the 5 species does not match the expected theoretical distribution.
3. **Degrees of Freedom**: 4
4. **P-value**: 0.05
5. **Does the data differ from expected distribution at the $$ \alpha=0.01 $$ significance level?**: No (fail to reject H0).
1. Null Hypothesis (H0): The observed distribution matches the expected distribution. 2. Alternative Hypothesis (H1): The observed distribution does not match the expected distribution. 3. Degrees of Freedom: 4 4. P-value: 0.05 5. Data differs from expected distribution at $$ \alpha=0.01 $$ significance level: No.

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