Vending machines on a college campus offer a variety of snacks.The purchasing agent believes that each type of snack is equally preferred by students and consequently orders equal quantities.The number of snacks sold from vending machines on this campus for the last six months is shown in the following tablE.The correct value of the test statistic for determining if the purchasing agent's belief if supported is

$\begin{array}{|l|l|l|l|l|}
\hline \text { Snack Type } & \text { Chips } & \text { Candy Bars } & \text { Crackers } & \text { Nuts } \
\hline \text { Purchase Frequency } & 159 & 198 & 174 & 149 \
\hline
\end{array}$

A) $\chi ^ { 2 } = 8.012$
B) $\chi ^ { 2 } = 12.019$
C) $\chi ^ { 2 } = 0.984$
D) $\chi ^ { 2 } = 45.014$
E) None of the above.

Question

Vending machines on a college campus offer a variety of snacks.The purchasing agent believes that each type of snack is equally preferred by students and consequently orders equal quantities.The number of snacks sold from vending machines on this campus for the last six months is shown in the following tablE.The correct value of the test statistic for determining if the purchasing agent's belief if supported is

\begin{array}{|l|l|l|l|l|}\hline \text { Snack Type } & \text { Chips } & \text { Candy Bars } & \text { Crackers } & \text { Nuts } \\\hline \text { Purchase Frequency } & 159 & 198 & 174 & 149 \\\hline\end{array}

$\begin{array}{|l|l|l|l|l|}
\hline \text { Snack Type } & \text { Chips } & \text { Candy Bars } & \text { Crackers } & \text { Nuts } \
\hline \text { Purchase Frequency } & 159 & 198 & 174 & 149 \
\hline
\end{array}$

A) $\chi ^ { 2 } = 8.012$
B) $\chi ^ { 2 } = 12.019$
C) $\chi ^ { 2 } = 0.984$
D) $\chi ^ { 2 } = 45.014$
E) None of the above.

Quizplus · Accepted Answer

To determine if the purchasing agent's belief is supported, we use a chi-square test for goodness of fit. The total number of snacks sold is $159 + 198 + 174 + 149 = 680$. With four types of snacks, the expected frequency for each type is $680 / 4 = 170$. The chi-square statistic is calculated as $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ is the observed frequency and $E_i$ is the expected frequency. Substituting the given values, we get $\chi^2 = \frac{(159-170)^2}{170} + \frac{(198-170)^2}{170} + \frac{(174-170)^2}{170} + \frac{(149-170)^2}{170} = 8.012$.

Vending Machines on a College Campus Offer a Variety of Snacks.The