Question

14. Molybdenum rods are produced by a production line setup. It is desir- able to check whether the process is in control. Let, X = length of such a rod. Assume X is approximately normally distributed with mean = and variance variance = 0, where the mean and variance are unknown. Take n = 400 sample rods, with sample average length x = 2 inches, and 2(x - )' = 399 In testing H, u = 2.2, H: # 2.2 tovar a = 5%, one should__the H, since the value lies the confidence interval. the distri b ution (A) not reject, 2.2, within (B) reject, 2, outside of (C) reject, 2.2, outside of (D) not reject, 2, within

Answer 1

giventhat sample size = n = 400, sample mean = 7 = 2, sample variance = sa = 2 200 then s= V399 20 H,:4 = 22 ¥1:47 2.2 (two tailed test) a: 5% (with 95% confidence) test statstic : 2 =-4-4 2-2.2 o s 399 / 2014 2007. =(-0.2)(20)=-4 To vn-1 1399 table value : 2 the table value for two tailed test with 95% confidence is 1.96 since P(-1.96 <Z <1.96) = 0.96 so Z =1.96 decision: since 2 =4>Z, the statstic Z located in critical region. hence H, is rejected the 95% confidence interval for u is (x-1.96-+1.96 m ) = (2-1996-*+1.967-1) =(1-196 -1•7+1.96-1) -(2-196(4):2+198( a)= (1902,2098) hence we should reject the H, sin ce the value 2.2lies out side of the confidence interval (1.902, 2.098) optionC.