chapter 1

Chapter 9: Inferences Based on Two Samples15.a. As either m or n increases, σ decreases, sopositive), sodecreases.⎛⎜ z⎝αµ−1− µσ2− ∆o⎟⎠⎞µ − µ 2− ∆oσ⎛β = Φ⎜z⎝decreases, so1increases (the numerator isαµ−1− µσ2− ∆o⎟⎠⎞b. As β decreases, zβincreases, and sincezβis the numerator of n , n increases also.16.x − y .2z = = . For n = 100, z = 1.41 and p-value = 2 [ 1− Φ( 1.41)] = . 1586 .2 2s s 21 2+n n nFor n = 400, z = 2.83 and p-value = .0046. From a practical point of view, the closeness of xand y suggests that there is essentially no difference between true average fracture toughnessfor type I and type I steels. The very small difference in sample averages has been magnifiedby the large sample sizes – statistical rather than practical significance. The p-value by itselfwould not have conveyed this message.Section 9.217.a.ν=2 2 25 6(10+10)2 2 25 6( ) ( )109+109237.21=.694 + 1.44= 17.43 ≈ 17b.ν=2 2 25 6(10+15)2 2 25 6( ) ( )109+1514224.01= = 21.7 ≈ 21.694 + .411c.ν=2 2 22 6(10+15)2 2 22 6( ) ( )109+151427.84= = 18.27 ≈18.018+.411d.ν =2 2 25 6( + )12 242 2 25 6( ) ( )1211+2423212.84= = 26.05 ≈ 26.395 + .098266