An insurance company is thinking about offering discounts on its life insurance
ID: 3159803 • Letter: A
Question
An insurance company is thinking about offering discounts on its life insurance policies to nonsmokers. As part of its analysis, it randomly selects 200 men who are 60 years old and asks them if they smoke at least one pack of cigarettes per day and if they have ever suffered from heart disease. The results are as follows:
Total
not HD
HD
Smokers
56
37
19
Non-smokers
144
119
25
Can the company conclude (a = 0.05) that smokers have a higher incidence of heart disease than non-smokers?
Total
not HD
HD
Smokers
56
37
19
Non-smokers
144
119
25
Explanation / Answer
Formulating the hypotheses
Ho: p1 - p2 <= 0
Ha: p1 - p2 > 0
Here, we see that pdo = 0 , the hypothesized population proportion difference.
Getting p1^ and p2^,
p1^ = x1/n1 = 19/56 = 0.339285714
p2 = x2/n2 = 25/144 = 0.173611111
Also, the standard error of the difference is
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] = 0.070706249
Thus,
z = [p1 - p2 - pdo]/sd = 2.343139488
As significance level = 0.05 , then the critical z is
zcrit = 1.644853627
Also, the p value is
P = 0.009561116
As z > 1.645, and P < 0.05, then we REJECT THE NULL HYPOTHESIS.
Hence, there is significant evidence that smokers have a higher incidence of heart disease than non-smokers at 0.05 level. [CONCLUSION]
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