Question

A researcher is interested in determining whether there is a correlation between number of packs of cigarettes smoked

# packs of cigarettes smoked (X)	(Y)
0	80
0	70
1	72
1	70
2	68
2	65
3	69
3	60
4	58
4	55

day and longevity (in years). n=10.

Answer 1

S.No	X	Y	(x-x̅)2	(y-y̅)2	(x-x̅)(y-y̅)
1	0	80	4.0000	176.89	-26.6000
2	0	70	4.0000	10.89	-6.6000
3	1	72	1.0000	28.09	-5.3000
4	1	70	1.0000	10.89	-3.3000
5	2	68	0.0000	1.69	0.0000
6	2	65	0.0000	2.89	0.0000
7	3	69	1.0000	5.29	2.3000
8	3	60	1.0000	44.89	-6.7000
9	4	58	4.0000	75.69	-17.4000
10	4	55	4.0000	136.89	-23.4000
Total	20	667	20.0000	494.10	-87.0000
Mean	2.000	66.70	SSX	SSY	SXY

null hypothesis: Ho:               ρ		=	0
Alternate Hypothesis: Ha: ρ		≠	0
0.05 level,two tail test and n-2= 8 df, critical t=			2.3060
Decision rule: reject Ho if absolute value of test statistic |t|>2.306
correlation coefficient r=		Sxy/(√Sxx*Syy) =-87/sqrt(20*494.10)=	-0.8752
test stat t=	r*(√(n-2)/(1-r2))=	-5.117

since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that there is a correlation between number of packs of cigarettes smoked and longevity (in years)