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 = 9 subjects with the syndrome, the average heat output was x = 0.61, and for n = 9 nonsufferers, the average output was 2.03. Let μ₁ and μ₂ denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with σ₁ = 0.3 and σ₂ = 0.4.

Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

Z=

P value=

(b) What is the probability of a type II error when the actual difference between μ₁ and μ₂ is

μ₁ − μ₂ = −1.3?

(Round your answer to four decimal places.)

Answer 1

Here

The test statistic can be written as

which under H₀ follows a standard normal distribution.

Now,

The value of the test statistic

and P-value

b) At 5% level of significance, The rejection region is :

P(Type II error)

= P(Accept H₀ when H₀ is not true)