Solution file for additional exercise 12.2
------------------------------------------

Planning of a study on energy metabolism in cows, with the aim of 
comparing treatment and control groups. The outcome is BHB
concentrations in milk, and the calculation is based on a single
observation of each cow. The standard deviation is estimated at 650, and the
effect of interest is 300. The output from Minitab's power menu (see appendix 
for Stata listing) gives the result.

MTB > Power;
SUBC>   TTwo;
SUBC>     Difference 300;
SUBC>     Power .8;
SUBC>     Sigma 650.
Power and Sample Size 

2-Sample t Test

Testing mean 1 = mean 2 (versus not =)
Calculating power for mean 1 = mean 2 + difference
Alpha = 0.05  Assumed standard deviation = 650

            Sample  Target
Difference    Size   Power  Actual Power
       300      75     0.8      0.801778

The sample size is for each group.

Comments:
---------
To obtain a power of 0.8, it is required to have 75 cows in each group,
and therefore a total of 150 cows. The researchers chose a total of 200
cows, possibly because of anticipated dropouts; in a partly observational 
study like this one it is difficult to keep dropout rates low.

---

Appendix: output from power calculation using Stata 13 menu:

. power twomeans 0, diff(300) sd(650)

Performing iteration ...

Estimated sample sizes for a two-sample means test
t test assuming sd1 = sd2 = sd
Ho: m2 = m1  versus  Ha: m2 != m1

Study parameters:

        alpha =    0.0500
        power =    0.8000
        delta =  300.0000
           m1 =    0.0000
           m2 =  300.0000
         diff =  300.0000
           sd =  650.0000

Estimated sample sizes:

            N =       150
  N per group =        75