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The data set labcomp .txt is the result of an "inter-lab" study where multiple labs, in this case each located at a different plant, participate in a study to compare measurements within and between the labs. For this study, the surface area of a silica was measured by each lab seven times. All labs had the capability of measuring using a 1-point CTAB procedure, and in addition two labs also measured using a 5-point CTAB procedure.
(a) Calculate summary statistics for each lab.
(b) Make side-by-side box plots comparing the labs (one for the 1-point data and one for the 5-point data)
(c) Make an error-bar chart of the data.
(d) Describe the distributions, and note any differences among the labs.
Let U1 and U2 be independent random variables. Suppose that U1 is χ2 with ν1 degrees of freedom while U = U1 + U2 is chi-square with ν degrees of freedom, where ν > ν1. Then prove that U2 is chi-square random variable with ν - ν1 degrees of freedom.
1. In the partially ordered set N × N with the ordering ( j, k) ≤ (m, n) iff j ≤ m and k ≤ n, consider the sequence (n, n), for n = 0, 1, 2,... . Describe all the maximal chains that include the given sequence. Do any of these chains have upper..
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