Problem:

n(d) = 38

\({{\bar{X}}_{1}}\) = 92

\({{\bar{X}}_{2}}\) = 95.5

\(\bar{d}\) = -3.5

\(s_{D}^{2}=21\)

a. Determine the values of t for which the null hypothesis \({{\mu }_{D}}={{\mu }_{1}}-{{\mu }_{2}}=0\), would be rejected for the alternative hypothesis, \({{\mu }_{D}}={{\mu }_{1}}-{{\mu }_{2}}<0\). Use \(\alpha \) = .10

b. draw appropriate conclusions.

c. find a 90% confidence interval for the mean difference \({{\mu }_{D}}\).