Question

CTE, Chronic traumatic encephalopathy, is a progressive degenerative brain disorder caused by repetitive brain trauma. A case controlled study examined the brains of deceased men with a diagnosed non-genetic degenerative disorder. The study compared individuals with and without a history of contact sports. Of the 66 men who had participated in contact sports, 21 had CTE. Two of the 132 men who had not participated in contact sports had CTE. What is the value of the test statistic for this chi-square test? Question options:

29.01

6.635

3.841

39.35

3.54

Answer 1

		Contact sports	Not contact sports	Total
CTE	Observed	21	2	23
	Expected	7.67	15.33	23.00
	O - E	13.33	-13.33	0.00
	(O - E)² / E	23.19	11.59	34.78
No CTE	Observed	45	130	175
	Expected	58.33	116.67	175.00
	O - E	-13.33	13.33	0.00
	(O - E)² / E	3.05	1.52	4.57
Total	Observed	66	132	198
	Expected	66.00	132.00	198.00
	O - E	0.00	0.00	0.00
	(O - E)² / E	26.24	13.12	39.35

Test Statistic :-
= Σ (Oi - Ei )2 / Ei
= 39.35