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 a cm min was measured. For m-g subjects with the syndrome, the average heat output was 0.64, and or n nonsufferers' respectively. Assume that the two distributions af heat output are normal with σ1-0.2 and σ2-0.3. 9 no sufferers the average output e true average heat outputs as 2 01 Let μ1 and μ2 denote or the su eres and (a) Consider testing Ho: μ1-μ2--1.0 versus Ha : μ1-#2くー1.0 at level 001. Describe in words what Ma says, and then carry Dut the test. OHa says that the average heat output for sufferers is less than1 al/mmin below that of non-sufferers O Ha says that the average heat output for sufferers is more than 1 cal/cm2/min below that of non-sufferers. Ha says that the average heat output for sufferers is the same as that of non-sufferers. Calculate the test statistic annd P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) P-value State the conclusion in the problem context. Fail to reject Ho. The data suggests that the average heat output for sufferers is less than 1 cal/cm2/min below that of non-sufferers Fail to rejoct Ho. The data suggests that the average heat output for sufferers is the same as that of non-sufferers. O Reject Ho. The data suggests that the average heat output for sufferers is more than 1 cal/cm*/min below that of non-sufferers Reject Ho. The data suggests that the average heat output for sufferers is the same as that of non-sufferers (b) What is the probability of a type II errar when the actual difference between μ1 and μ2 is μι-μ2--1.4? (Round Your answer to four decimal places-) (C) Assuming that m-n, what sample sizes are required to ensure that β-0.1 when μι-μΖ--1.4? (Round your answer up to the nearest whole number.) subjects

Answer 1

tA Shen daha o ¥. Ļlosang-thar-the ave rage heat output fev Suferes ia move -te st. statistic: mt nm e-GY-2.01)-(-1,0) 1.3千t/.

-from z table 0.0010 The Concluslon nhe paoblem Cont . e heat butput 1 O 2 6.3 -D 3 233- 0 t2

2.1- (-2-5) 0.42.86 Assume mn. -find thc ^ample. Sizes ,气 n m

12 O.L , 0.1 hWheu Ö.2 pl_ 2.33 0-2 m)

-3.33 + -02 O 13 o13 0 3.6 2 m냔.sog)"