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 14.86 .
What is the null hypothesis?
Select
What is the alternative hypothesis?
Welect
What is the number of degrees of freedom? Ex: 5
Does the data differ from expected distribution at the significance level?
Select

Ask by Lee Nunez. in the United States
Dec 17,2024

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  • Null Hypothesis: The observed distribution matches the expected distribution.
  • Alternative Hypothesis: The observed distribution does not match the expected distribution.
  • Degrees of Freedom: 4
  • Data differs from expected distribution at ? Yes

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Mind Expander

The null hypothesis for a chi-square test typically states that there is no significant difference between the observed and expected frequencies of the species distribution. Essentially, it suggests that any observed variance is due to random chance.
On the flip side, the alternative hypothesis posits that there is a significant difference between the observed and expected frequencies, indicating that the distribution among the species is not what was anticipated.
To find the degrees of freedom, you can use the formula , where is the number of categories (species in this case). With 5 species, this results in .
Finally, comparing the test statistic to the critical value from the chi-square distribution table at the level and 4 degrees of freedom, you would find the critical value (which is approximately 9.488). Since 14.86 is greater than 9.488, you would reject the null hypothesis, indicating that the data does differ from the expected distribution.
For a lively wrap-up, please remember that statistical tests are like detective work! You’re piecing together clues (data) to unravel the mystery of whether your guesses about species distribution hold water or not! And if they do not, it’s like the universe saying, “Surprise! Nature doesn’t always follow your script!”

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