Question

The article “Determination of Carboxyhemoglobin Levels and Health Effects on Officers Working at the Istanbul Bosphorus Bridge” (G. Kocasoy and H. Yalin, Journal of Environmental Science and Health, 2004:1129–1139) presents assessments of health outcomes of people working in an environment with high levels of carbon monoxide (CO). Following are the numbers of workers reporting various symptoms, categorized by work shift. The numbers were read from a graph.

	Morning Shift	Evening Shift	Night Shift
Influenza	16	13	18
Headache	24	33	6
Weakness	11	16	5
Shortness of Breath	7	9	9

Can you conclude that the proportions of workers with the various symptoms differ among the shifts?

(a) State the appropriate null hypothesis.

(b) Compute the expected values under the null hypothesis.

(c) Compute the value of the chi-square statistic.

(d) Find the p-value. What do you conclude?

Answer 1

a)

null hypothesis : proportions of workers with the various symptoms are same  among the shifts

b)

Observed	Oi	mornign shift	evening shift	Night shift	Total
	Influenza	16	13	18	47
	headaches\	24	33	6	63
	weakness	11	16	5	32
	shortness of breath	7	9	9	25
	Total	58	71	38	167
Expected	Ei=Σrow*Σcolumn/Σtotal	mornign shift	evening shift	Night shift	Total
	Influenza	16.323	19.982	10.695	47
	headaches\	21.880	26.784	14.335	63
	weakness	11.114	13.605	7.281	32
	shortness of breath	8.683	10.629	5.689	25
	Total	58	71	38	167

c)

chi square    χ2	=(Oi-Ei)2/Ei	mornign shift	evening shift	Night shift	Total
	Influenza	0.010	2.440	4.990	7.440
	headaches\	0.210	1.440	4.850	6.500
	weakness	0.000	0.420	0.710	1.130
	shortness of breath	0.330	0.250	1.930	2.510
	Total	0.550	4.550	12.480	17.580

d)

degree of freedom(df) =(rows-1)*(columns-1)=

6

for 6 df and above test statistic p value =0.0074

as p value is signfiicantly low we reject null hypothesis

we have sufficient evidence to conclude that  proportions of workers with the various symptoms differ among the shifts