Question

2. Use the Chi-Square test procedure to solve the following research question: A psychologist seeks to examine whether certain mental health issues are more prevalent in a sample of violent criminal offenders (1,000) compared to the average population.

	Observed	Expected
Anxiety disorder	152	146 (14.6 x 1000)
Mood disorder	112	80 (8.0 x 1000)
Personality disorder	195	90 (9.0 x 1000)
Schizophrenia	75	15 (1.5 x 1000)
None	521	669 (66.9 x 1000)

2a. Calculate and provide the chi-square statistic for this data (4 pts)

2b. State the degrees of freedom and determine if the test is significant (2 pts)

Answer 1

Answer2: Use the Chi-Square test procedure to solve the following research question: A psychologist seeks to examine whether certain mental health issues are more prevalent in a sample of violent criminal offenders (1,000) compared to the average population.

The hypothesis test:

Ho: The certain mental health issues are more prevalent in a sample of violent criminal offenders (1,000) compared to the average population.

Ha: The certain mental health issues are not more prevalent in a sample of violent criminal offenders (1,000) compared to the average population.

a) Test statistic χ2:

Test statistic χ2 = Σ(Observed value - Expected value)^2 / Expected value

	Observed (O)	Expected (E)	(O-E)^2/E
Anexiet disorder	152	146	0.2466
Mood disorder	112	80	12.8
Personality disorder	195	90	122.5
Schizophrenia	75	15	240
None	521	669	32.7414
Total	1055	1000	408.288

Therefore,

Test statistic χ2 = 408.288

b) degree of freedom, df

df = (r-1)(c-1)

df = (5-1)(2-1)

df = 4

P-value from test statistic χ2 and df

P-value = 0.00001

Assuming significance level α = 0.05

Since P-value (0.0000) < α (0.05) significance level.

The test is significant.

Reject Ho. There is sufficient evidence to conclude that certain mental health issues are not more prevalent in a sample of violent criminal offenders (1,000) compared to the average population.