chapter 1

CHAPTER 9Section 9.11.a. E ( X − Y ) = E( X ) − E( Y ) = 4.1−4.5 = −.4, irrespective of sample sizes.σ=mof X − Y = . 0724 = . 2691 .b. V ( X − Y ) = V ( X ) + V ( Y )2( 1.8) ( 2.0)2 22σ1 2+ = + =n100100.0724, and the s.d.c. A normal curve with mean and s.d. as given in a and b (because m = n = 100, the CLTimplies that both X and Y have approximately normal distributions, soX − Y doesalso). The shape is not necessarily that of a normal curve when m = n = 10, because theCLT cannot be invoked. So if the two lifetime population distributions are not normal,the distribution ofX − Y will typically be quite complicated.2. The test statistic value isx − yz = , and H o will be rejected if either ≥1. 962 2s s1 +m n42,500 − 40,400 2100z ≤ −1.96 . We compute == = 4. 85222200 1900 433.33+45 452z orz . Since 4.85 >1.96, reject H o and conclude that the two brands differ with respect to true average tread lives.3. The test statistic value isz ≥ 2.33. We compute( x − y)− 5000z2 2s1s2+m n( 43,500 − 36,800)−5000z ==222200 1500+45 45= , and H o will be rejected at level .01 if700396.93= 1.76> 2.33, so we don’t reject H o and conclude that the true average life for radials does notexceed that for economy brand by more than 500., which is not261