Chapter 9.5, Problem 1Q

Historically, fluctuations in the amount of rare metals found in coins are not uncommon $\left(82\right)$. The following data may be a case in point. Listed are the silver percentages found in samples of a Byzantine coin minted on two separate occasions during the reign of Manuel I $\left(1143–1180\right)$. Construct a 90% confidence interval for ${\mu }_X-{\mu }_Y$, the true average difference in the coin’s silver content ( $=$ “early”−“late”). What does the interval imply about the outcome of testing $H_0:{\mu }_X={\mu }_Y$? For these data $s_X=0.54$ and $s_Y=0.36$.

Early Coinage, $x_i$ $\left(\%\text{ Ag}\right)$	Late Coinage, $y_i$ $\left(\%\text{ Ag}\right)$
5.9	5.3
6.8	5.6
6.4	5.5
7.0	5.1
6.6	6.2
7.7	5.8
7.2	5.8
6.9
6.2
Average: 6.7	Average: 5.6