Chi-Squared Test Question 5

At a local ice-cream store, 210 people were surveyed on whether they preferred eating ice cream from a cone or a cup. Of the 210 people surveyed, 70 were adults and 140 were children. Of the responses, 150 indicated the cone as the preferred method of eating ice cream. For those surveyed, there was no association between age and preferred method of eating ice cream. Which of the following tables shows the distribution of responses?

\begin{array}{|r|c|c|c|} \hline & \text{Cone} & \text{Cup} & \text{Total} \\ \hline \text{Adults} & 35 & 35 & 70 \\ \hline \text{Children} & 115 & 25 & 140 \\ \hline \text{Total} & 150 & 60 & 210 \\ \hline \end{array}

\begin{array}{|r|c|c|c|} \hline & \text{Cone} & \text{Cup} & \text{Total} \\ \hline \text{Adults} & 40 & 30 & 70 \\ \hline \text{Children} & 110 & 30 & 140 \\ \hline \text{Total} & 150 & 60 & 210 \\ \hline \end{array}

\begin{array}{|r|c|c|c|} \hline & \text{Cone} & \text{Cup} & \text{Total} \\ \hline \text{Adults} & 50 & 20 & 70 \\ \hline \text{Children} & 100 & 40 & 140 \\ \hline \text{Total} & 150 & 60 & 210 \\ \hline \end{array}

\begin{array}{|r|c|c|c|} \hline & \text{Cone} & \text{Cup} & \text{Total} \\ \hline \text{Adults} & 60 & 10 & 70 \\ \hline \text{Children} & 90 & 50 & 140 \\ \hline \text{Total} & 150 & 60 & 210 \\ \hline \end{array}

Approach

If there is no association between age and preferred eating method, we should expect the same proportion of adults and children to eat with cones or cups.

\frac{\text{Cone}}{\text{Total}} = \frac{150}{210}

\frac{\text{Adults that eat with cone}}{\text{Adults}} = \frac{x}{70} = \frac{150}{210}

x = 50 \text{ Adults that eat with cone}

A similar calculation can be done for the children.