Preferences for the type of diet drink from a random sample of 121 shoppers are in the table below. A researcher is interested in determining if there is a relationship between the type of diet drink preferred and the age of the shoppers. $$\begin{array} { l l | r | r | r }
& & \text { Under } 25 & 25 \text { and Older } & \text { Total } \
\hline \text { Diet Pepsi } & \text { Observed } & 10 & 60 & 70 \
& \text { Expected } & 21.40 & 48.60 & 70.00 \
& \% \text { of chisq } & 28.6 \% & 12.6 \% & 41.3 \% \
\hline \text { Diet Coke } & \text { Observed } & 18 & 14 & 32 \
& \text { Expected } & 9.79 & 22.21 & 32.00 \
& \text { \% of chisq } & 32.5 \% & 14.3 \% & 46.8 \% \
\hline \text { Diet Sprite } & \text { Observed } & 9 & 10 & 19 \
& \text { Expected } & 5.81 & 13.19 & 19.00 \
& \% \text { of chisq } & 8.3 \% & 3.6 \% & 11.9 \% \
\hline \text { Total } & \text { Observed } & 37 & 84 & 121 \
& \text { Expected } & 37.00 & 84.00 & 121.00 \
& \% \text { of chisq } & 69.4 \% & 30.6 \% & 100.0 \% \
& & & & \
& & 21.21 \text { chi-square } &
\end{array}$$ What can you conclude for the data analysis at ? = .05?
A)The means are equal for all three groups.
B)There is insufficient evidence to conclude that the type of drink and age are dependent.
C)Conclude that the type of drink and age are dependent.
D)No conclusion is possible without knowing the p-value.

Question

Preferences for the type of diet drink from a random sample of 121 shoppers are in the table below. A researcher is interested in determining if there is a relationship between the type of diet drink preferred and the age of the shoppers. $$\begin{array} { l l | r | r | r } 
& & \text { Under } 25 & 25 \text { and Older } & \text { Total } \
\hline \text { Diet Pepsi } & \text { Observed } & 10 & 60 & 70 \
& \text { Expected } & 21.40 & 48.60 & 70.00 \
& \% \text { of chisq } & 28.6 \% & 12.6 \% & 41.3 \% \
\hline \text { Diet Coke } & \text { Observed } & 18 & 14 & 32 \
& \text { Expected } & 9.79 & 22.21 & 32.00 \
& \text { \% of chisq } & 32.5 \% & 14.3 \% & 46.8 \% \
\hline \text { Diet Sprite } & \text { Observed } & 9 & 10 & 19 \
& \text { Expected } & 5.81 & 13.19 & 19.00 \
& \% \text { of chisq } & 8.3 \% & 3.6 \% & 11.9 \% \
\hline \text { Total } & \text { Observed } & 37 & 84 & 121 \
& \text { Expected } & 37.00 & 84.00 & 121.00 \
& \% \text { of chisq } & 69.4 \% & 30.6 \% & 100.0 \% \
& & & & \
& & 21.21 \text { chi-square } &
\end{array}$$ What can you conclude for the data analysis at ? = .05?
A)The means are equal for all three groups.
B)There is insufficient evidence to conclude that the type of drink and age are dependent.
C)Conclude that the type of drink and age are dependent.
D)No conclusion is possible without knowing the p-value.

Quizplus · Accepted Answer

The table shows the results of a chi-square test of independence. The expected values are calculated assuming that there is no relationship between the type of drink and age. The chi-square test statistic is calculated by comparing the observed values to the expected values. The degrees of freedom for this test are (r - 1)(c - 1) = (3 - 1)(2 - 1) = 2. 
The chi-square test statistic of 21.21 with 2 degrees of freedom is significant at α = .05 (p-value < .05). This indicates that the observed frequencies are not consistent with the null hypothesis that there is no relationship between the type of drink and age. Therefore, we can conclude that the type of drink and age are dependent.

Preferences for the Type of Diet Drink from a Random