# Using a Contingency Table to determine Independence

The transportation committee for a large industrial complex wanted to study the mode of transportation used by male and female employees. The following data was obtained.

Sex Drive Alone Carpool Public Trans Total

Male 160 72.5 17.5 250

Female 160 72.5 17.5 250

Total 320 145 35 500

Using the table provided, is there a relationship between sex and mode of transportation? Formulate and test the appropriate hypothesis?

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#### Solution Preview

A: See the attached Word Document for a cleaner solution, using Math fonts.

The Table above is called a Contingency Table. The first step to solving the problem is to calculate the expected probabilities for each cell (ex. males that drive alone, males that use a carpool, etc.). To start this off - to find the expected value of the cell for males that drive alone, we use this formula

(R1*C1)/n = (250*320)/500 = 160.

R1 = 1st row total

C1 = 1st column total

The expected value for next one - males that use carpool is

(R1*C2)/n = (250*145)/500 = 72.5.

The rest of the table of expected values looks like the following. ...

#### Solution Summary

A step by step solution is provided in which we illustrate the use of a contingency table to test for independence. Construction of the contingency table with expected values and the calculation of the test statistic are illustrated with an example.