Persons having Raynaud\'s syndrome are apt to suffer a sudden impairment of bloo

Question

Persons having Raynaud'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 = 8 subjects with the syndrome, the average heat output was x = 0.64, and for n = 8 nonsufferers, the average output was 2.07. Let 1 and 2 denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with 1 = 0.2 and 2 = 0.4.

a) What is the probability of a type II error when the actual difference between 1 and 2 is 1 2 = 1.2?

b)Assuming that m = n, what sample sizes are required to ensure that = 0.1 when

1 2 = 1.2?

Explanation / Answer

Solution;

a. Type ii error

= P (Z -2.33|µ1 - µ2 = -1.2)

   = P [(X-bar – Y-bar – (-1) – (1 - 1.2)/1^2/m + 2^2/n -2.33 – (1 – 1.2)/0.2^2/10 + 0.4^2/10 ]

   = P [Z -0.92]

= 1 – P [Z -0.92]

= 1 – 0.1788

= 0.8212

b. P (Z -2.33 + 0.2/0.2^2/n + 0.4^2/n)

P (Z 2.33 - n( 0.2/0.2^2 + 0.4^2)) = 0.1

P (Z -1.28) = 0.1

2.33 - n ( 0.2/0.2^2 + 0.4^2) = -1.28

n = (2.33 + 1.28)^2(0.2^2 + 0.4^2)/0.2^2

n = 65.16 ~ 66

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.