EXAMPLE 10.9 I Cement Hydration An article in the journal Hazardous Waste and Hazardous Materials (1989, Vol. 6) reported the results of an analysis of the weight of calcium in standard cement and cement doped with lead. Reduced levels of calcium would indicate that the hydration mechanism in the cement is blocked and would allow water to attack various locations in the cement structure. Ten samples of standard cement had an average weight percent calcium of ( ar{x}_{1}=90.0 ) with a sample standard deviation of ( s_{1}=5.0 ), and 15 samples of the lead-doped cement had an average weight percent calcium of ( ar{x}_{2}=87.0 ) with a sample standard deviation of ( s_{2}=4.0 ). We assume that weight percent calcium is normally distributed and find a ( 95 % ) confidence interval on the difference in means, ( mu_{1}-mu_{2} ), for the two types of cement. Furthermore, we assume that both normal populations have the same standard deviation.
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For standard cement, we have \( n_{1}=10, \bar{x}_{1}=90.0, s_{1}=5.0 \). For lead-doped cement, we have \( n_{2}=15, \bar{x}_{2}=87.0, s_{2}=4.0 \). Show more…
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