Q1 H0: mua-mub=0
   Ha: mua-mub<0

   ybara-ybarb=-8 hence consistent with Ha

   s(ybara-ybarb)=2.525
   z=-3.168

   p-value = 0.08% hence highly signif and so reject H0.

Q2 a. YES, since H0 was rejected. The 80% CI is:
 
      -8 +/- 1.3(2.525) 

      Hence the 80% CI is [-11.2825, -4.7175] and so I am 80% confident that 
      the difference in population means is between -11.2825 and -4.7175.

   b. Note that in order to solve this problem you assume n1=n2=n and
      sigma1=sigma2=sigma. Now, n=(z(99)^2*s^2*2)/delta^2 and z(99)=2.6,
      delta=2 but s must be determined. Since s1 and s2 are available
      from the previous problem then they may be used to determine s
      and so we compute s by pooling s1 and s2. Therefore:
      
      s = sqrt((35(100)+39(144))/74)=11.099

      n=2.6^2*11.099^2*2/2^2=416.38 so 417 required for each sample.

Q3 Since n1 and n2 are small then we will assume normality and equal
   variances to proceed. Given the equal variance assumption we will pool
   s1 and s2.
 
   s(p)=sqrt((19(100)+19(144))/38)=11.045

   s(ybara-ybarb)=3.493
   z=-2.29

   p-value btw 1% and 2.5% hence signif and so reject H0.