Share
Explore BrainMass

# Chi square - Random Samples of Different Scenarios

1. A public policy researcher would like to know whether spending on cities and spending on the environment are statistically dependent. The following data were collected from a random sample of constituents in the voting district.

2. The US Department of Justice wanted to determine whether the sex of a person murdered is related to the sex of the person committing the murder. Their 1993 report on crime stated the following

3. A high school guidance counselor wants to test whether there is a relationship between sex and profession.

4. A therapist would like to know whether there is a relationship between the type of mental illness and drug of choice for drug users.

#### Solution Preview

1. A public policy researcher would like to know whether spending on cities and spending on the environment are statistically dependent. The following data were collected from a random sample of constituents in the voting district.

Spending on the Environment
Spending on Cities Decrease Increase Total
Decrease 24 157 181
Increase 5 108 113
29 265 294

Solution:

a. Complete the following table:

Spending on the Environment
Spending on Cities Decrease Increase
Decrease Obs 24 157
Exp 29*181/294=17.85 265*181/294=163.15
Increase Obs 5 108
Exp 29*113/294=11.15 265*113/294=101.85

B. How many degrees of freedom?
(2-1)*(2-1) = 1
C. What is the value of χ2 for the data?

Cell 1,1 = =2.12 Cell 1,2 = =0.23
Cell 2,1 = =3.39 Cell 2,2 = =1.22
Total =6.96

D. Are the two forms of government spending related?

Critical value is 3.841at 5% level of significance.

Since calculated value is more than critical value we conclude that two forms of government spending are related

E Examine the data using the Adjusted Residual technique. What are the adjusted residuals for the four cells? Which of the cells contributes most to the dependence between the two forms of government spending?

Cell 1,1 =2.12 Cell 1,2 =0.23 Cell 2,1 =3.39 Cell 2,2 ...

#### Solution Summary

The solution determines whether spending on the environment or spending on cities are statistically dependent. The US department of justice examines the sex of a person murdered and its relationship to the sex of the person committing a murder. The relationship between sex and profession is also examined. Lastly, the relationship between the type of mental illness and drug of choice for drug users is determined.

\$2.19