In studying the occurrence of genetic characteristics, the following sample data were_ obtained. You would like to test the claim that the characteristics occur with the same
Frequency at the 0.05 significance level. What is value of the test statistic? $\begin{array}{l|cccccc}
\text { Characteristic } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \
\hline \text { Frequency } & 28 & 30 & 45 & 48 & 39 & 39
\end{array}$

A) $\chi ^ { 2 } = 8.263$
B) $\chi ^ { 2 } = 5.991$
C) $t = 8.263$
D) $\chi ^ { 2 } = 5.821$

Question

In studying the occurrence of genetic characteristics, the following sample data were_ obtained. You would like to test the claim that the characteristics occur with the same
Frequency at the 0.05 significance level. What is value of the test statistic? $\begin{array}{l|cccccc}
\text { Characteristic } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \
\hline \text { Frequency } & 28 & 30 & 45 & 48 & 39 & 39
\end{array}$

A) $\chi ^ { 2 } = 8.263$
B) $\chi ^ { 2 } = 5.991$
C) $t = 8.263$
D) $\chi ^ { 2 } = 5.821$

Quizplus · Accepted Answer

The test statistic is calculated using the chi-square ($\chi^2$) formula for goodness of fit, which compares observed frequencies with expected frequencies. Given the frequencies for characteristics A through F, we first calculate the total number of observations and then determine the expected frequency for each characteristic assuming they occur with the same frequency. The $\chi^2$ value is then calculated by summing the squared differences between observed and expected frequencies, divided by the expected frequency for each characteristic. The correct calculation leads to a $\chi^2$ value of 8.263, making option A the correct choice.

In Studying the Occurrence of Genetic Characteristics, the Following Sample