Question

Consider the following hypotheses. HO HS 207 HA > 207 A sample is to be taken from a population with conditions given in parts a through c. a. n= 10 b. n = 30 mean of 211 and a standard deviation of 6. The hypothesis test is to be conducted using a significance level of 0.05. Determine the probability of committing a Type Il error for the c. n = 50 a. The probability of committing a Type Il error is (Round to four decimal places as needed.) b. The probability of committing a Type Il error is (Round to four decimal places as needed.) c. The probability of committing a Type Il error is (Round to four decimal places as needed.)

Answer 1

Solution Given hypotheses ase!. Hoi u < 207 Hii M > 207 from a and It is also given that a sample is taken population with mean of 211 Standard deviation of 6. we have to determine the probability of type-II esror at a= oros. First, we find the resection region Sample mean. region for For n=10; we resect fits z = x-lo 7 Zoios 71 To * - 207 libus b/7o =) # 7 207 + 16454 210:11 Hence, we resect the role hyrothesis is 587721-17 Probability of type II eshora P(Allepot Hol M=211) =P(X < 210ill | 4=211) Now,

9 7) P 18-211 < 210111- 2!! 21. bo ) P(Z <-0.469.0) 0.3195 Hence, Probability of tybe I error for N-,lo is 0.32 2 ) for n=30 2 = X 207 61930 7, 1.643 Y 7, 207 + lobus. 6 =) > > 208.802 Hence, we reject Ho, if X7, 208.802 How, Probability of type-I essor = Placcept Hol M=211) FPC < 208.802 / 211 ) Pla z < 208.802-211 ?") 6/132 = P(Z < -2.006) 0.002

Hence, Probability of typer II esrar for N2 30 is Oooo2 $) For nosos 2- - 207 6/550 7 libus 7, 207 + 1645. b 550 =) > > 208.3952 Hence, we reject Ho, if X 71208.395 Now, Probability of type-II esror = Placcept Hol M=211) =P(X<208.395 l M=211) - P(X- 211 < 208.39-211 61050 6/75. = P(Z <-3.075 = Oiool Hence, Probability of type-I essor for Na so es ooool