Question

with high levels of Carbon monoxide (Co. F Shifts Night Morn 26 24 62. Influenza Headache 32 Symptoms 29 60 and work shift At 5% signica nce level can you conclude that there is a relationship between the

Answer 1

Given table data is as below

MATRIX	col1	col2	col3	TOTALS
row 1	26	13	18	57
row 2	24	32	6	62
row 3	10	16	5	31
TOTALS	60	61	29	N = 150

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calculation formula for E table matrix

E-TABLE	col1	col2	col3
row 1	row1*col1/N	row1*col2/N	row1*col3/N
row 2	row2*col1/N	row2*col2/N	row2*col3/N
row 3	row3*col1/N	row3*col2/N	row3*col3/N

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expected frequecies calculated by applying E - table matrix formulae

E-TABLE	col1	col2	col3
row 1	22.8	23.18	11.02
row 2	24.8	25.213	11.987
row 3	12.4	12.607	5.993

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calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above

Oi	Ei	Oi-Ei	(Oi-Ei)^2	(Oi-Ei)^2/Ei
26	22.8	3.2	10.24	0.449
13	23.18	-10.18	103.632	4.471
18	11.02	6.98	48.72	4.421
24	24.8	-0.8	0.64	0.026
32	25.213	6.787	46.063	1.827
6	11.987	-5.987	35.844	2.99
10	12.4	-2.4	5.76	0.465
16	12.607	3.393	11.512	0.913
5	5.993	-0.993	0.986	0.165
				chi^2 o = 15.727

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set up null vs alternative as

null, Ho: no relation b/w symptoms and the work shift

alternative, H1: exists a relation b/w symptoms and the work shift

level of significance, ? = 0.05

from standard normal table, chi square value at right tailed, chi^2 ?/2 =9.488

since our test is right tailed,reject Ho when chi^2 o > 9.488

we use test statistic chi^2 o = ?(Oi-Ei)^2/Ei

from the table , chi^2 o = 15.727

critical value

the value of |chi^2 ?| at los 0.05 with d.f (r-1)(c-1)= ( 3 -1 ) * ( 3 - 1 ) = 2 * 2 = 4 is 9.488

we got | chi^2| =15.727 & | chi^2 ? | =9.488

make decision

hence value of | chi^2 o | > | chi^2 ?| and here we reject Ho

chi^2 p_value =0.003

ANSWERS

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null, Ho: no relation b/w symptoms and the work shift

alternative, H1: exists a relation b/w symptoms and the work shift

test statistic: 15.727

critical value: 9.488

p-value:0.003

decision: reject Ho

conclude that exists a relation b/w symptoms and the work shift