Following is a set of observed and expected frequencies: ) $\begin{array}{l|lllll}
\text { Observed } & 5 & 18 & 26 & 23 & 16 \
\hline \text { Expected } & 10 & 15 & 30 & 15 & 10
\end{array}$

Test the hypothesis that the distribution of the observed frequencies is as given by the expected frequencies. Use the $\alpha = 0.05$ level of significance.
A) Reject $H _ { 0 }$.
B) Do not reject $H _ { 0 }$.

Question

Following is a set of observed and expected frequencies: ) $\begin{array}{l|lllll}
\text { Observed } & 5 & 18 & 26 & 23 & 16 \
\hline \text { Expected } & 10 & 15 & 30 & 15 & 10
\end{array}$

Test the hypothesis that the distribution of the observed frequencies is as given by the expected frequencies. Use the $\alpha = 0.05$ level of significance.
A) Reject $H _ { 0 }$.
B) Do not reject $H _ { 0 }$.

Quizplus · Accepted Answer

To test the hypothesis, we use the chi-square test for goodness of fit. The chi-square statistic is calculated using the formula $\chi^2 = \sum \frac{(O - E)^2}{E}$, where $O$ is the observed frequency and $E$ is the expected frequency. Calculating this for each category and summing gives a chi-square value. This value is then compared to the critical value from the chi-square distribution table with the appropriate degrees of freedom (df = number of categories - 1 = 5 - 1 = 4) and the given level of significance ($\alpha = 0.05$). If the calculated chi-square value is greater than the critical value, we reject the null hypothesis ($H_0$), indicating that the observed frequencies significantly differ from the expected frequencies. Given the data, the calculated chi-square value would indeed suggest a significant difference, leading to the rejection of $H_0$.

Following Is a Set of Observed and Expected Frequencies: ) Observed 518262316 Expected 1015301510\begin{array}{l|lllll}\text { Observed } & 5 & 18 & 26 & 23 & 16 \\\hline \text { Expected } & 10 & 15 & 30 & 15 & 10\end{array} Observed Expected ​510​1815​2630​2315​1610​​

Following Is a Set of Observed and Expected Frequencies: ) $\begin{array}{l|lllll}\text { Observed } & 5 & 18 & 26 & 23 & 16 \\\hline \text { Expected } & 10 & 15 & 30 & 15 & 10\end{array}$