4. You believe there may be a relationship between a household’s income and whet
ID: 3376158 • Letter: 4
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