Related questions with answers

The two-way frequency table below represents the results of a survey about ways students get to school.

\begin{matrix} \text{ } & \text{Type of Transportation}\\ \text{Grade} & \text{On Foot} & \text{By Car} & \text{By Bus} & \text{Total}\\ \text{9} & \text{15} & \text{28} & \text{64} & \text{107}\\ \text{10} & \text{20} & \text{30} & \text{43} & \text{93}\\ \text{Total} & \text{35} & \text{58} & \text{107} & \text{200}\\ \end{matrix}

Given grade level, is that person more or less likely to travel to school by bus? Explain your response.

The two-way frequency table below represents the results of a survey about favorite forms of entertainment. Write fractions that are not simplified as responses.

\begin{matrix} \text{ } & \text{Like Board Games}\\ \text{Like Reading} & \text{Yes} & \text{No} & \text{Total}\\ \text{Yes} & \text{48} & \text{25} & \text{73}\\ \text{No} & \text{43} & \text{9} & \text{52}\\ \text{Total} & \text{91} & \text{34} & \text{125}\\ \end{matrix}

Given someone interested in reading, is that person more or less likely to take an interest in playing board games? Explain.

A researcher surveyed 135 people, 85 females and 50 males. The researcher asked each person which of the following types of movies they preferred: action, comedy, or drama. Complete the table.

\begin{array}{c}\\ \text{Favorite Type of Movie} \\ \begin{array}{|c|c|c|c|c|} \hline \text { Gender } & \text { Action } & \text { Comedy } & \text { Drama } & \text { Total } \\ \hline \text { Female } & 35 & & 18 & \\ \hline \text { Male } & 12 & 28 & & \\ \hline \text { Total } & & & 28 & \\ \hline \end{array} \end{array}

Question

What does it mean to say there is an association between characteristics in a two-way frequency table?

Solution

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It means that the conditional relative frequency for two given characteristics is different than the marginal relative frequency for one of the characteristics. An example of this was in exercise 9.