Question

 Persons having Reynaud’s syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output (cal/cm2/min) was measured. For m = 10 subjects with the syndrome, the average heat output was ¯x = 0.64 with sample standard deviation 0.2, and for n = 10 nonsufferers, the average output was 2.05 , with sample standard deviation 0.4. Let µ1 and µ2 denote the true average heat outputs for the two types of subjects. Assume that the two distributions of heat output are normal with equal variance

(a) Build a 95% confidence interval for µ1 − µ2. 

(b) Test, under significance level 5%, the null hypothesis that µ1 = µ2, against the alternative hypothesis that µ1 ̸= µ2.

(c) Test, under significance level 5%, the null hypothesis that σ 2 1 = σ 2 2 , against the alternative hypothesis that σ 2 1 ̸= σ 2 2 .

Answer 1