Question

Page 4 Example: An analyst is conducting a test involving the following hypotheses Horn = 100 vs. Hu # 100 The population is known to be normally distributed with a standard deviation of 3. Assume that the sample size is 9. Suppose the acceptance region is 98.5 < X < 101.5, a. Find the Type I error b. Calculate the probability of making a Type II error if the population mean actually equals 103.

Answer 1

1 n 12 - i. Sol", Given thell, Somple size, nog popvariance - 3'zg. 302 pop" mean : det x,.... Xg be novo with E G-H)N M601) x + 4 tu, 9) then ^ = xWMCM, 1) , varex) = 2 necepiece Region: 98.5, Ås 101.5a Type -I errorm Reject Ho when it a true Under He: 2100 1 98.5-100 < -1004 104.5-IVO -1.5 4241.5" 12151.5 - Aceptamee Ryon so Type -I errore 121 21.5 Any: rejection Region ond Pl Typer-I error) = PI Reject Hol Hois true) = l-p1121315) 1-2.pf6241,5) = 1-2x0.4332 21-0.8664 = 0.1336 Rop(Type- serror) 20:1336 Ary: © Pitype Ferror] = p[ Accept Ho | H, is true) Trinen = P1 98.54811015/h) 5103 = Pſ 98.5–10338-103510154103) =pl-4.52 26-15) = Rd. -06-1:5).–14(-4.5) = 4(15)- $14.5) - 011295 -0.000L ..(-2): 462) Tpl Type .cr error) = 0112947 LIITUNUD 17