In 1965 a silver shortage in the United States prompted Congress to authorize the minting of silver less dimes and quarters. They also recommended that the silver content of half-dollars be reduced from 90% to 40%. Historically, fluctuations in the amount of rare metals found in coins are not uncommon (76). 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 (1143–1180). Construct a 90% confidence interval for μ_X − μ_Y, the true average difference in the coin’s silver content (=“early”− “late”). What does the interval imply about the outcome of testing H₀: μ_X = μ_Y? For these data s_X = 0.54 and s_Y = 0.36.

Early Coinage, x_i                             Late Coinage, y_i

(% Ag)                                     (% Ag)

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