Historically, fluctuations in the amount of rare metals found in coins are not uncommon (82). 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 out come of testing H₀: μ_X = μ_Y ? For these data s_X = 0.54 and s_Y = 0.36.

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Early Coinage, xi (% Ag) 5.9 6.8 6.4 7.0 6.6 7.7 7.2 6.9 6.2 Average: 6.7 Late Coinage, yi (% Ag) 5.3 5.6 5.5 5.1 6.2 5.8 5.8 Average: 5.6