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 11.143 .
What is the null hypothesis?
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What is the alternative hypothesis?
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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?
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The null hypothesis claims that there is no significant difference between the observed distribution of species and the expected theoretical distribution, meaning any variation is due to random chance. The alternative hypothesis, on the other hand, proposes that there is a significant difference between the observed and expected distributions, indicating that something other than chance is influencing the observed frequencies.

To calculate the degrees of freedom for this test, you will take the number of categories (in this case, species) and subtract one. Therefore, with 5 species, the degrees of freedom will be . For the p-value, you’d typically consult a chi-square distribution table or use software to find the probability corresponding to your test statistic of 11.143 with 4 degrees of freedom. If the p-value is less than 0.05, you would reject the null hypothesis, indicating that the data significantly differs from the expected distribution. Given the chi-square value, it is likely that you would reject the null hypothesis at the significance level.