Question

5. h

The next problem comes directly from a student project from three years ago. It is on a very serious topic so I am putting it last on the final.

A former student in Math& 146 did a project that asked people whether they had ever committed a crime, whether they were convicted, and whether they suffered from mental health problems. She thought there would be an association between being convicted and having mental health problems. She collected data through a confidential survey in her office, and then she also collected data from homeless people through in-person interviews.

The table below shows all people in her sample who said they committed a crime.

• The row variable is whether they were convicted or not convicted
• The column variable is whether they had mental health problems:   no or yes   

	No - Mental Health Problems	Yes - Mental Health Problems	Total
Convicted	20	22
Not convicted	27	16
Total

Does the data suggest there is an association between being convicted of a crime and having mental health problems? Provide a comprehensive answer using concepts from two-way tables and probabilities. For full credit, explain at least one possible source of bias in this research.

Answer 1

	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	no	yes	F	P			Total
convicted	47*42/85=23.224	38*42/85=18.776					42
not convicted	47*43/85=23.776	38*43/85=19.224					43

	(fo-fe)^2/fe
convicted	0.447	0.553
not convicted	0.437	0.541

Ho: given two variable are independent
H1: Given two variables are not independent

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   1.978                          
                              
Level of Significance =   0.05                          
Number of Rows =   2                          
Number of Columns =   2                          
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 2- 1 ) =   1                          
                              
p-Value =   0.1596   [Excel function: =CHISQ.DIST.RT(χ²,df) ]                      
Decision:    p value > α , do not reject Ho                          

There is not sufficient evidence that there is an association between being convicted of a crime and having mental health problems

Response bias could a major concern

THANKS

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