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?

Answer 1

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

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

The expected frequencies are
	One car	More than one car	Total
Low Income	57.75	52.25	110
High income	47.25	42.75	90
Total	105	95	200

The chisquare contribution values are

Oi	Ei	(Oi-Ei)^2 /Ei
80	57.75	8.5725
30	52.25	9.4749
25	47.25	10.4775
65	42.75	11.5804
	Total:	40.1053

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