Smoking increases the risk of developing more than 50 serious health conditions. Some may be fatal,...

Smoking increases the risk of developing more than 50 serious health conditions. Some may be fatal, and others can cause irreversible long-term health damage.
It is hypothesized that smoking may cause wrinkles around eyes. The smoking behaviour and the information about wrinkles around eyes are recorded and the following frequency table is obtained.

Heavy wrinkles Moderate wrinkles No wrinkles

Heavy smoker 95 5 50

Light or nonsmoker 103 7 240

Do these data show association between smoking and wrinkles around eyes? Formulate a suitable statistical model and a statistical hypothesis test to analyse these data, and state your conclusion

Expert Solution

ANSWER::

Ho: given two variable are independent
H1: Given two variables are not independent

...........

Chi-Square Test of independence
	Observed Frequencies

	heavy wrinkle	moderate wrinkle	no wrinkle	Total
heavy smoker	95	5	54	154
light smoker	103	7	240	350




Total	198	12	294	504

	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	heavy wrinkle	moderate wrinkle	no wrinkle	Total
heavy smoker	198*154/504=60.5	12*154/504=3.667	294*154/504=89.833	154
light smoker	198*350/504=137.5	12*350/504=8.333	294*350/504=204.167	350




Total	198	12	294	504

(fo-fe)^2/fe	heavy wrinkle	moderate wrinkle	no wrinkle
heavy smoker	19.674	0.485	14.293
light smoker	8.656	0.213	6.289

................

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   49.6107

Level of Significance =   0.05
Number of Rows =   2
Number of Columns =   3
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 3- 1 ) =   2

p-Value =   0.0000
Decision:    p-value < α , Reject Ho

...............

so, there is association between smoking and wrinkle around eyes.

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