Question 1085998
Ho: mean 1<= mean 2, meaning liquid diet causes less or the same weight loss as powder.
Ha:mean 1>mean 2
alpha=0.05 P{reject Ho|ho true}
2 sample t test where (x1 bar-x2 bar)/SE will give a t-statistic with df=83, 0.95, 1 df lost from each group.
Test statistic for 1 way test is t>1.644.  Reject if t >1.644, otherwise fail to reject.
t=(45-42)/SE
SE is sqrt (s1^2/n1 + (s2^2/n2))=sqrt (196/36 + 144/49=sqrt(8.38)=2.895
t=3/2.895=1.036
p-value=0.15.  That means if the Ho is true, we would have a 15% chance of finding a result this great or more.  Since we require a 5% chance or less, we fail to reject Ho.
CI=1.644*2.895=4.76
One way confidence interval is 4.76 should be < the difference in the means.  It is not.  If a two way confidence interval is desired, there has to be a two way test, and here the question implies a one way test.  A two way test would have the question: "is there a difference between the powder and the liquid?"