Waist-to-hip ratio was measured on 8 men just before they entered a weight loss program (time 1) and again 6 months after the program (time 2).  The results are below.

          Subject           1          2         3          4         5          6         7          8

          Time 1          1.03     0.99     1.18     0.82     1.02     1.05     1.06     0.82

          Time 2          1.00     1.02     1.12     0.78     1.06     1.00     1.08     0.76

data one;

    input WHR1 WHR2;

    diff = WHR1 - WHR2;

Datalines;

1.03 1.00

0.99 1.02

1.18 1.12

0.82 0.78

1.02 1.06

1.05 1.00

1.06 1.08

0.82 0.76

;

run;

a. Calculate the difference for each subject (as time 1 value minus time 2 value), then calculate the mean and standard deviation of these differences.  You can do this however you like.

b. Using the information from part (a), "by hand", calculate a 90% confidence interval for the difference of the means for the two time periods (i.e., for the mean difference).

c. We want to use a paired t-test, at a = .05, to test if the mean waist-to-hip ratio is smaller at time 2 than at time 1 (i.e., test if the program is effective).  Use PROC TTEST to obtain the test statistic and p-value.  Turn in the printout.

d. A colleague looks at the printout and decides that we have proven that the program is not effective.  Do you agree with his conclusion?  Why or why not?