Following is a set of observed and expected frequencies:

$\begin{array} { l | l l l l l } \text { Observed } & 10 & 20 & 26 & 30 & 19 \\\hline \text { Expected } & 10 & 10 & 20 & 20 & 15\end{array}$

Test the hypothesis that the distribution of the observed frequencies is as given by the expected frequ Use the $\alpha = 0.01$ level of significance.

Question

Following is a set of observed and expected frequencies:

\begin{array} { l | l l l l l } \text { Observed } & 10 & 20 & 26 & 30 & 19 \\\hline \text { Expected } & 10 & 10 & 20 & 20 & 15\end{array}

Test the hypothesis that the distribution of the observed frequencies is as given by the expected frequ Use the

\alpha = 0.01

level of significance.

Quizplus · Accepted Answer

To test the hypothesis that the observed frequencies follow the expected frequencies, we use the chi-square test. The chi-square statistic is calculated using the formula $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ and $E_i$ are the observed and expected frequencies, respectively. Calculating this for each category and summing them up gives us the chi-square statistic. Comparing this statistic to the critical value from the chi-square distribution table with the appropriate degrees of freedom (in this case, $df = n - 1 = 5 - 1 = 4$) and the given $\alpha = 0.01$ level of significance allows us to decide whether to reject the null hypothesis. If the calculated chi-square statistic is greater than the critical value, we reject the null hypothesis, indicating that the observed frequencies significantly differ from the expected frequencies. Given the data, the calculation would likely show a significant difference, leading to the rejection of the null hypothesis that the observed frequencies follow the expected distribution.

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Following Is a Set of Observed and Expected Frequencies $\begin{array} { l | l l l l l } \text { Observed } & 10 & 20 & 26 & 30 & 19 \\\hline \text { Expected } & 10 & 10 & 20 & 20 & 15\end{array}$