Question

1. The amount of time it takes a patient to fully recover from a virus-inflicted illness (in days) follows a normal distribution with unknown mean i and a variance equal to 9m?. Find the most powerful test to verify the null hypothesis that i = k against the alternative that = 2k on the base of k independent observations, for a significance level of n%. Calculate the power of this test (for the alternative hypothesis). What is the result of the testing procedure, if in the observed sample the average duration of recovery amounted to k + m + 2n days? ANSWER: critical region of the test: Power of the test: Reject null? (YES/NO): Solution:
k＝28 n＝1 m＝15

Answer 1

solutions given dator К= 28 1 - 45 500 төг As As a Qa - slissus ܕܦܠܥܠܪܕܝ fully recoved from the о Х СР, а) <br> to 9ь Aь с няк VSH gör=2K

28 HoM XON CM,45=6) VISHA:M = 56 > 28 Jest statistic (2) z = z - 28 45 1528 where c = 45 2 - 45 - 28 45528 - > 1.999 ,2=0.01 (17) sritical Region 2-33 since 2= 1.999 L 2-33 Reject nella No > Power PCE >KIMI=56) Whela K = 287 2:33x 45 528 -> K= 47.814 -:P (2> 47.814-56 45 1528 out POWER G 0:31 P(Z > -0.9625) 4 0.8321 -4-3-2-1 0 1 2 3 -0.9625 X