2. To compare the corrosion-resistance properties of two types of máterial used

Question

2. To compare the corrosion-resistance properties of two types of máterial used in under- ground pipelines, specimens of both types are buried in soil for a 2-year period and the maximum penetration for each specimen is measured. A sample of size n 48 specimens ofrnaterial type A yielded X1 = 0.49 and Si = 0.19; a sample of size n2-42 specimens of miaterial type B gave X2 = 0.36 and S2 = 0.16. (a) What is 0.49-0.36 = 0.13 an estimate of? (b) Assuming that the two samples are independent, compute the standard standard error of X1 X2.

Explanation / Answer

(a) Sample mean of material type A = 0.49 and for type B = 0.36

Sample mean A - Sample mean B is an estimate of differences between the sample means i.e we can compare the means of two independent groups, if both sample sizes are at least 30 , then the sampling distribution can be estimated using the t distribution.

(b) Standard error for difference in mean between two independent samples = SEx1-x2 = sqrt [ s21 / n1 + s22 / n2 ]

=(0.192 /48 + 0.162 /42)0.5

=0.0369

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