Question

Altamura, Dell'Osso, Vismara, and Mundo (2008) measured the relationship between gender and duration of untreated illness (DUI) among a sample of those suffering from major depressive disorder (MDD). The following table lists the observed frequencies from this study.

		Duration of Untreated Illness
		DUI ≤ 12 Months	DUI > 12 Months
Gender	Men	20	5	25
	Women	55	33	88
		75	38	N = 113

Compute a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal places.)
=  

Decide whether to retain or reject the null hypothesis.

Retain the null hypothesis.Reject the null hypothesis.     

Answer 1

The Expected value data are in the table below. Each Cell = Row total * Column Total/N. N = 133

	DUI <= 12	DUI > 12	Total
Men	20	5	25
Women	55	33	88
Total	75	38	113
Expected
	DUI <= 12	DUI > 12	Total
Men	16.59	8.41	25
Women	58.41	29.59	88
Total	75	38	113

The degrees of freedom, df = (r – 1) * (c -1) = (2 - 1) * (2 - 1) = 1

The Hypothesis:

H0: There is no relation between gender and duration of untreated illness.

Ha: There is a relation between gender and duration of untreated illness.

The Test Statistic: The table below gives the calculation of .

Number	Observed	Expected	(O-E)	(O-E)2	(O-E)2/E
1	20	16.59	3.41	11.60819171	0.6996
2	55	58.41	-3.41	11.60819171	0.1987
3	5	8.41	-3.41	11.60819171	1.3808
4	33	29.59	3.41	11.60819171	0.3923
Total					2.67

test = 2.67

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The Critical Value:   The critical value at = 0.05,df= 1, critical = 3.842

The p value: The p value: The p value at test = 2.67, df = 1; P value = 0.1023

The Decision Rule: If test is > critical, then Reject H0.

If p value is < , Then Reject H0.

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The Decision: Since test (2.67) is < critical (3.842), We retain the Null Hypothesis

Since p value (0.1023) is > (0.05), We retain the Null Hypothesis

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The Conclusion: There isn't sufficient evidence at the 95% significance level to conclude that there is a relation between gender and duration of untreated illness.

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