Pregunta
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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 7.779 .
What is the null hypothesis?
The observed distribution and the expected distribution do not differ v
What is the alternative hypothesis?
The mean of the random variable is zero
What is the number of degrees of freedom? Ex: 5 .
What is the -value? Ex: 1.23 .
Does the data differ from expected distribution at the significance level?

Ask by Wade Jimenez. in the United States
Dec 17,2024

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  1. Null Hypothesis ( ): The observed distribution and the expected distribution do not differ significantly.
  2. Alternative Hypothesis ( ): The observed distribution differs significantly from the expected distribution.
  3. Number of Degrees of Freedom: 4.
  4. -value: 0.1.
  5. Conclusion: At , the null hypothesis is not rejected, indicating no significant difference between the observed and expected distributions.

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Beyond the Answer

The null hypothesis in this scenario posits that the observed distribution of the species matches the expected theoretical distribution, meaning there is no significant difference between them. Essentially, any variation in the counts can be attributed to random chance alone.
To find the degrees of freedom, you would typically use the formula , where is the number of categories or species being tested. In this case, with 5 species, the degrees of freedom would be .
For the -value, you would need to refer to a chi-square distribution table or use statistical software to determine it based on the test statistic of 7.779 and the 4 degrees of freedom. Assuming you find a -value less than 0.05, you would reject the null hypothesis, indicating that the observed data significantly differs from the expected distribution at the significance level.

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