Question

An insurance company collected data from a class of high school sophomores on whether or not they have a cell phone and whether or not they have a car. The two-way table below shows the data collected.
Calculate the relative frequency of the data to determine which association the two-way table suggests.
A. Those who do not have a car tend to have a cell phone.

B. Those who have a car tend not to have a cell phone.

C. Those who have a car tend to have a cell phone.

D. None of the associations listed are correct.

Answer 1

Answer:

C. Those who have a car tend to have a cell phone.

Step-by-step explanation:

The relative frequency for a data set n is calculated by dividing each frequency $x_i$ by n.

We have a table that relates the use of cars and cell phones.

First, we take from the table the population that has a car.

$n = 18$

Then, of the students who have a car, 12 have a cell phone and 6 do not have a cell phone.

Then we calculate the relative frequencies $f_{x_i}$ for those who have a cell phone and those who do not.

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Relative frequency   Students with car  n = 18.

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Cell phone     No cell phone      Total n

 12/18                    6/18                     18

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Relative frequency   Students with car  n = 18.

-------------------------------------------------- --------------------------------------

Cell phone     No cell phone      Total n

  0.666              0.333                   18

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Most students who have a car also have a cell phone.

Now we calculate the relative frequency for students who do not have a car.

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Relative frequency  Students without a car  n = 7

-------------------------------------------------- --------------------------------------

Cell phone       No cell phone             Total  n

 2/7                     5/7                          7

_______________________________________________  

_______________________________________________

Relative frequency  Students without a car  n = 7

-------------------------------------------------- --------------------------------------

Cell phone        No cell phone           Total  n

 0.286                 0.714                              7

_______________________________________________

Most students who do not have a car do not have a cell phone either.

Then these data suggest that. Those who have a car tend to have a cell phone.

Option C