chapter 1

Chapter 9: Inferences Based on Two Samples87. ∆ = 00 , = σ 10σ , d = 1,1 2=200 14.142 ⎛ nσ = = , son n⎟ ⎞= Φ⎜1.645 −⎝ 14.142 ⎠β ,giving β = .9015, .8264, .0294, and .0000 for n = 25, 100, 2500, and 10,000 respectively. Iftheµ s referred to true average IQ’s resulting from two different conditions, µ − µ 1i '1 2=would have little practical significance, yet very large sample sizes would yield statisticalsignificance in this situation.88. µ − µ 0H is tested against µ − µ 00:1 2=H using the two-sample t test,a:1 2≠t025,15or if t ≤ −2. 131 . With = 11. 20s1= 2.68 , y = 9. 79 , s2= 3. 21 , and m = n = 8, s p = 2.96, and t = .95, so H o is notrejecting H o at level .05 if either ≥ t .= 2. 131x ,rejected. In the situation described, the effect of carpeting would be mixed up with anyeffects due to the different types of hospitals, so no separate assessment could be made. Theexperiment should have been designed so that a separate assessment could be obtained (e.g., arandomized block design).H : p = p0 will be rejected at level α in favor of H a: p1> p2if either250167z ≥ z .= 1.645 . With p = . 10 , p = . 0668 , and ˆ = . 083489.1 205.0332z = = 4.2.0079name than for a black name.ˆ1 =2500ˆ2=2500p ,, so H o is rejected . It appears that a response is more likely for a white34 − 4690. The computed value of Z is z = = −1.34 . A lower tailed test would be34 + 46Φ −1 .34 = .0901>.appropriate, so the p-value ( ) 05be effective.= , so we would not judge the drug to292