chapter 1

Chapter 8: Tests of Hypotheses Based on a Single Sample17.20,960 − 20,000150016a. z == 2.56 > 2. 33 so reject H o .⎛20,000 − 20,500⎞b. β ( 20 ,500):Φ⎜2.33+⎟ = Φ( 1.00) = . 8413c. ( 20,500)⎝1500/16⎠( 2.33+1.645)⎡1500⎤β = .05 : n = ⎢= 142.220,000 20,500⎥ , so use n = 143⎣ − ⎦d. α = 1 − Φ( 2.56) = . 0052218.72.3 − 75a. = −1.5 so 72.3 is 1.5 SD’s (of x ) below 75.1.8b. H o is rejected if z ≤ −2. 33 ; since z = −1. 5 is not −2. 33c. =≤ , don’t reject H o .α area under standard normal curve below –2.88 = Φ( − 2 .88) = . 0020⎛⎜⎝75 − 70 ⎞⎟9 /5 ⎠d. Φ − 2 .88 + = Φ( − .1) = . 4602 so β ( 70 ) = . 5398e.( 2.88 + 2.33)2⎡9⎤n == 87.95 , so use n = 88⎢ 75 70 ⎥⎣ − ⎦f. ( 76) = P(Z < −2.33α when µ = 76 ) = P(X < 72. 9 when µ = 76)⎛ 72.9 − 76 ⎞= Φ⎜⎟ = Φ −⎝ .9 ⎠( 3.44) = . 0003243