Associations in Categorical Data

ID: tokuv-nofoh
Created by Illustrative MathIllustrative Math
Subject: Algebra, Algebra 2
Grade: 8-9

Associations in Categorical Data

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Problem 1

1) Which value would best fit in the missing cell to suggest there is no evidence of an association between the variables?

digital watchanalog watchdisplays the date5427no date display18\begin{array}{|c|c|c|} \hline \\[-1em] &\textbf{digital watch} & \textbf{analog watch} \\[-1em] \\ \hline \\[-1em] \textbf{displays the date} & 54 & 27 \\[-1em] \\ \hline \\[-1em] \textbf{no date display} & 18 & \\[-1em] \\ \hline \end{array}

a) 9\text{9}b) 18\text{18}c) 27\text{27}d) 54\text{54}
Problem 2

The relative frequency table shows the percentage of each type of art (painting or sculpture) in a museum that would classify in the different styles (modern or classical).

modernclassicalpaintings41%59%sculptures38%62%\begin{array}{|c|c|c|} \hline \\[-1em] & \textbf{modern} & \textbf{classical} \\[-1em] \\ \hline \\[-1em] \textbf{paintings} & 41\% & 59\% \\[-1em] \\ \hline \\[-1em] \textbf{sculptures} & 38\% & 62\% \\[-1em] \\ \hline \end{array}

2) Based on these percentages, is there evidence to suggest an association between the variables?

True or false? Write below.

3) Explain your reasoning.

Problem 3

An automobile dealership keeps track of the number of cars and trucks they have for sale, as well as whether they are new or used.

cartrucknew812233used42251\begin{array}{|c|c|c|} \hline \\[-1em] & \textbf{car} & \textbf{truck} \\[-1em] \\ \hline \\[-1em] \textbf{new} & 812 & 233 \\[-1em] \\ \hline \\[-1em] \textbf{used} & 422 & 51 \\[-1em] \\ \hline \end{array}

4) Based on the data, does there appear to be an association between the type of automobile and whether it is new or used?

True or false? Write below.

5) Explain your reasoning.

Problem 4

A survey is given to 1,432 people about whether they take daily supplemental vitamins and whether they eat breakfast on a regular basis. The results are shown in the table.

take daily vitaminsno daily vitamineat breakfast384476no breakfast268304\begin{array}{|c|c|c|} \hline \\[-1em] & \textbf{take daily vitamins} & \textbf{no daily vitamin} \\[-1em] \\ \hline \\[-1em] \textbf{eat breakfast} & 384 & 476 \\[-1em] \\ \hline \\[-1em] \textbf{no breakfast} & 268 & 304 \\[-1em] \\ \hline \end{array}

Create a relative frequency table that shows the percentage of the entire group that is in each cell. Find the values that belong in the labeled cells in the table, rounding to the nearest whole percent.

take daily vitaminsno daily vitaminseat breakfastABno breakfastCD\begin{array}{|c|c|c|} \hline \\[-1em] & \textbf{take daily vitamins} & \textbf{no daily vitamins} \\[-1em] \\ \hline \\[-1em] \textbf{eat breakfast} & \text{A} & \text{B} \\[-1em] \\ \hline \\[-1em] \textbf{no breakfast} & \text{C} & \text{D} \\[-1em] \\ \hline \end{array}

6) Cell A

7) Cell B

8) Cell C

9) Cell D

Problem 5

Several college students are surveyed about their college location and preferred locations for a spring break trip.

college near the coastcollege away from the coastbeach break3754ski break2436\begin{array}{|c|c|c|} \hline \\[-1em] & \textbf{college near the coast} & \textbf{college away from the coast} \\[-1em] \\ \hline \\[-1em] \textbf{beach break} & 37 & 54 \\[-1em] \\ \hline \\[-1em] \textbf{ski break} & 24 & 36 \\[-1em] \\ \hline \end{array}

10) What percentage of people who prefer to spend spring break at the beach go to a college away from the coast?

11) What percentage of people who prefer to spend spring break skiing go to a college away from the coast?

Problem 6

A group of people are surveyed about whether they prefer to bike or run to exercise, and whether they prefer summer or winter weather. The results are in the table.

bikerunsummer108212winter98\begin{array}{|c|c|c|} \hline \\[-1em] & \textbf{bike} & \textbf{run} \\[-1em] \\ \hline \\[-1em] \textbf{summer} & 108 & 212 \\[-1em] \\ \hline \\[-1em] \textbf{winter} & & 98 \\[-1em] \\ \hline \end{array}

12) What value could go in the blank cell so that the percentage of people who like to bike and also prefer winter weather is 10%?