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/cm^{2}/min) was measured. For m = 10 subjects
with the syndrome, the average heat output was x = 0.64,
and for n = 10 nonsufferers, the average output was 2.08.
Let Î¼_{1} and Î¼_{2} denote the
true average heat outputs for the sufferers and nonsufferers,
respectively. Assume that the two distributions of heat output are
normal with Ïƒ_{1} = 0.2 and Ïƒ_{2}
= 0.4.
A) 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 Î¼_{1} âˆ’ Î¼_{2} = âˆ’1.2? (Round your answer to four decimal places.)
(c) Assuming that m = n, what sample sizes are Î¼_{1} âˆ’ Î¼_{2} = âˆ’1.2? (Round your answer up to the nearest whole number.) |