(Solved): Identify the critical value. a. Perform a chi-square test using \( \alpha=0.05 \) to determine if ...

Identify the critical value.

a. Perform a chi-square test using \( \alpha=0.05 \) to determine if the observed frequencies follow a discrete probability distribution. Determine the null and alternative hypotheses. Choose the correct answer below. A. \( \mathrm{H}_{0} \) : The distribution of the variable differs from the normal distribution. \( \mathrm{H}_{1} \) : The distribution of the variable is the normal distribution. B. \( \mathrm{H}_{0} \) : The expected frequencies are all equal to 5 . \( \mathrm{H}_{1} \) : At least one expected frequency differs from 5. C. \( \mathrm{H}_{0} \) : The distribution of the variable is the same as the given distribution. \( \mathrm{H}_{1} \) : The distribution of the variable differs from the given distribution. D. \( \mathrm{H}_{0} \) : The distribution of the variable differs from the given distribution. \( \mathrm{H}_{1} \) : The distribution of the variable is the same as the given distribution. Compute the value of the test statistic, \( \chi^{2} \). \[ \gamma^{2}=8.082 \] (Round to two decimal places as needed.) Identify the critical value. The critical value is (Round to two decimal places as needed.)