Fundamentals of Probability and Statistics for Engineers

(John Hannent) #1

10.9 Problem 8.2(c) gives 100 measurements of time gaps (see Table 8.4). On the basis
of these data, postulate a likely distribution for X and test your hypothesis at the
5% significance level.


10.10 Consider the data given in Problem 8.2(d) for the sum of two consecutive time
gaps. Postulate a likely distribution for X and test your hypothesis at the 5%
significance level.


10.11 Problem 8.2(e) gives data for one-minute vehicle arrivals (see Table 8.5). Postulate
a likely distribution for X and test your hypothesis at the 5% significance level.


10.12 Problem 8.2(h) gives a histogram for X, the peak co mbustion pressure (see Figure
8.4). On the basis of these data, postulate a likely distribution for X and test your
hypothesis at the 5% significance level.


10.13 Suppose that the number of drivers sampled is200. Based on the histogram given
in Problem 8.2(i) (see Figure 8.5), postulate a likely distribution for X 1 and test
your hypothesis at the 1% significance level.


10.14 Problem 8.2(j) gives a histogram for X, the number of blemishes in television tubes
(see Fi gure 8.6). On the basis of this sample, postulate a likely distribution for X
and test your hypothesis at the 5% significance level.


10.15 A total of 24 readings of the annual sediment load (in 10^6 tons) in the Colorado
River at the Grand Canyon are (arranged in increasing order of magnitude) 49,
50, 50, 66, 70, 75, 84, 85, 98, 118, 122, 135, 143, 146, 157, 172, 177, 190, 225, 235,
265, 270, 400, 480. U sing the K olmogorov–Smirnov test at the 5% significance
level, test the hypothesis that the annual sediment load follows a lognormal
distribution (data are taken from Beard, 1962).


10.16 For the snowfall data given in Problem 8.2(g) (see Table 8.6), use the K olmo-
gorov–Smirnov test and test the normal distribution hypothesis on the basis of
snowfall data from 1909–2002.


Model Verification 333

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