As part of a project to develop measurement standards for asbestos concentration

Question

As part of a project to develop measurement standards for asbestos concentration, we wanted to count the asbestos fibers on filters. For this purpose, we dissolved asbestos in water and spread it on a filter. From the filter, we then took a punch of 3mm diameter in each of 23 grid squares, mounted it on a transmisson electron microscope and counted the number of fibers. As a result, we observed the following:

31 29 19 18 31 28 34 27 34 30
16 18 26 27 27 18 24 22 28 24
21 17 24

Formulate a decision problem. Construct a statistical decision problem.

Explanation / Answer

We compute the test statistic t: t = x¯ µ s n = 24.91 18 5.48 23 t = 6.05 We find the rejection region. Here we use significance level = 0.05 with n 1 = 23 1 = 22 degrees of freedom. Therefore the rejection region is when t < 2.074 or t > 2.074. Conclusion: Since t = 6.05 falls in one of the rejection regions we reject H0. Compute the pvalue of the test: This is a two-sided test therefore the pvalue is pvalue= 2P(X >¯ 24.91) = 2P(t > 6.05). From the t table we can only say that pvalue is less that 0.01.

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