A new weight$-$reducing technique, consisting of a liquid protein diet, is currently undergoing tests by the Food and Drug Administration $($FDA$)$ before its introduction into the market. The weights fo a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for $3$ weeks.

                             before      after

Person $1$                  $149,$  $\mathrm{ \; \; \; 1}42$

Person $2194,189$

Person $3187,184$

Person $4196,190$

Person $5203,199$

Summary information is as follows: d $=5,$ sd $=1\mathrm{.}58$

Calculate a $90\%$ confidence interval for the difference between the mean weights before and after the diet is used.