4. You believe there may be a relationship between a household’s income and whet

Question

4. You believe there may be a relationship between a household’s income and whether it possesses more than one car. You have conducted a survey of 200 families and you have discovered the following:

Low income families with one car: 80

Low income families with more than one car: 30

High income families with one car: 25

High income families with more than one car: 65

a. State the null and alternate hypotheses in plain English sentences (not equations).

b. What is the calculated chi-squared value?   Show your calculations.

c. The tabled chi-squared value for 5% significance and one degree of freedom is 3.84. Can you reject the null hypothesis? Why or why not?

Explanation / Answer

a) H0: There is no relationship between a household’s income and whether it possesses more than one car

H1: There is relationship between a household’s income and whether it possesses more than one car

Let the los be alpha = 5%

b) From the given data

The chisquare contribution values are

Degrees of freedom: 1

Test Statistic, X^2: 40.1053
Critical X^2: 3.841456

Here Chisquare value > Chisquare critical value so we reject H0

Thus we conclude that there is relationship between a household’s income and whether it possesses more than one car

One car More than one car Total Low Income 80 30 110 High income 25 65 90 Total 105 95 200

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