Explain random system component is adequately represented, Operation Management

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Suppose 40 observations of a random system component have been recorded as shown in the table below (these numbers are sorted).

0.0345 0.1079 0.1313 0.1452 0.1788 0.2101 0.2249 0.2351 0.2389 0.2487

0.2684 0.2891 0.3011 0.3254 0.3518 0.3614 0.4418 0.4559 0.4803 0.4989

0.5314 0.5542 0.5563 0.5841 0.5942 0.6157 0.6895 0.7160 0.7212 0.7428

0.7624 0.7788 0.8212 0.8452 0.8645 0.8691 0.9011 0.9124 0.9348 0.9842

b. Using k = 8, perform a 2 c goodness-of-fit test that this random system component is adequately represented with a U[0,1] distribution.

Suppose 100,000 random numbers from the same random component have been recorded, and performing the same test with k = 250 (even though this is outside the guidelines for k) obtains the test statistic = 207.19. Does this change the conclusion (obtained from 40 observations)?


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