Heart Disease and Obesity in American Samoan Men. The study described in Section

Question

Heart Disease and Obesity in American Samoan Men. The study described in Section 18.1.1 also included men. The data for men are shown in the accompanying table. (a) Compute (i) the sample proportions of CVD deaths for the obese and nonobese groups; (ii) the standard error for the difference in sample proportions; (iii) a 95% confidence interval for the difference in popula- tion proportions. (b) Find a one-sided p-value for the test of equal population proportions (using the standard error already computed). (c) Compute (i) the sample odds of CVD death for the obese and nonobese groups; (ii) the estimated odds ratio; (iii) the standard error of the estimated log odds ratio; (iv) a 95% confidence interval for the odds ratio, (d) Write a concluding sentence that incorporates the confidence interval from part (c). CVD death Yes 1,179 1,409 Obese Not obese 1-22 2

Explanation / Answer

(a)
Sample proportion of infantile paralysis for the placebo group = 142 / (142 + 199858) = 0.00071 = 0.071 %
Sample proportion of infantile paralysis for the Salk polio vaccine group = 56 / (56 + 199944) = 0.00028 = 0.028 %

(b)
Pooled sample proportion is, p = (p1 * n1 + p2 * n2) / (n1 + n2)
where p1 and p2 are the proportions for placebo and Salk polio vaccine group
and n1 and n2 are the sample size of placebo and Salk polio vaccine group
n1 = 142 + 199858 = 200000
n2 = 56 + 199944 = 200000
p = (0.071 * 200000 + 0.028 * 200000) / (200000 + 200000) = 0.0495 % = 0.000495

The standard error (SE) of the sampling distribution difference between two proportions.
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }

SE = sqrt{ 0.000495 * ( 1 - 0.000495 ) * [ (1/200000) + (1/200000) ] } = 0.00007034

(c)
Difference in means = 0.00071 - 0.00028 = 0.00043
Z value for 95% confidence interval is 1.96
95% confidence interval is,
(0.00043 - 1.96 * 0.00007034, 0.00043 + 1.96 * 0.00007034)
(0.0002921, 0.0005679)

(d)
Test statistic, z = (p1 - p2) / SE
= 0.00043 / 0.00007034 = 6.113165

One - sided P-value is given as,
P(z > 6.113165) = 4.883715 x 10-10

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