Question

An article in the journal Hazardous Waste and Hazardous Materials (Vol. 6, 1989) 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 90.0, with a sample standard deviation of 5.0 and 15 samples of the lead-doped cement had an average weight percent calcium of 87.0 with a sample standard deviation of 4.0.

Is there evidence to support a claim that doping the cement with lead changes the mean weight of calcium in the cement?

Answer 1

H₀:

H₁:

The test statistic t = ()/sqrt(s1^2/n1 + s2^2/n2)

                             = (90 - 87)/sqrt((5)^2/10 + (4)^2/15)

                             = 1.59

df = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1)

     = ((5)^2/10 + (4)^2/15)^2/(((5)^2/10)^2/9 + ((4)^2/15)^2/14)

     = 16

At alpha = 0.05, the critical values are t_{0.025, 16} = +/- 2.120

Since the test statistic value is not greater than the critical value(1.59 < 2.12), so we should not reject H₀.

So there is not sufficient evidence to support the claim that doping the cement with lead changes the mean weight of calcium in the cement.