Preferences for the Type of Diet Drink from a Random

question 55

Multiple Choice

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. $$\begin{array}{l}\begin{array} { l l | r | r | r } & & \text { Under } 25 & 25 \text { and Older } & \text { Total } \\\hline \text { Diet Pepsi } & \text { Observed } & 10 & 60 & 70 \\& \text { Expected } & 21.40 & 48.60 & 70.00 \\& \% \text { of chisq } & 28.6 \% & 12.6 \% & 41.3 \% \\\hline \text { Diet Coke } & \text { Observed } & 18 & 14 & 32 \\& \text { Expected } & 9.79 & 22.21 & 32.00 \\& \% \text { of chisq } & 32.5 \% & 14.3 \% & 46.8 \% \\\hline \text { Diet Sprite } & \text { Observed } & 9 & 10 & 19 \\& \text { Expected } & 5.81 & 13.19 & 19.00 \\& \text { \% of chisq } & 8.3 \% & 3.6 \% & 11.9 \% \\\hline \text { Total } & \text { Observed } & 37 & 84 & 121 \\& \text { Expected } & 37.00 & 84.00 & 121.00 \\& \text { \% of chisq } & 69.4 \% & 30.6 \% & 100.0 \%\end{array}\\\text { 21.21 chi-square }\end{array}$$ In performing a chi-square test of independence on these data, how many degrees of freedom will the test statistic have?

• A)1
• B)2
• C)4
• D)6

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Definitions:

Mean Shoe Life

The average lifespan of a shoe, measured by duration of usage before it becomes unwearable, typically calculated from a sample.

Marathon Training

A structured program of physical exercises and running practice aimed at preparing an individual to complete a marathon.

Standard Deviation

A measure of the amount of variation or dispersion of a set of values, indicating how much the members of the set diverge from the mean.

Z-Score

A statistical measure that describes a value's relationship to the mean of a group of values, measured in terms of standard deviations from the mean.