HW-3_solutions

HW-3_solutions - PROBLEM 4.11 Data of Table 4.8, Column 1 N...

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4-20 PROBLEM 4.11 KNOWN: Data of Table 4.8, Column 1 N = 20 FIND: F ± tS F (95%) SOLUTION For this dataset in Column 1: with 11 9 N ν =−= . Then from Table 4.4, t 19,95 = 2.093. The scatter of the measured data set can be expressed by 1 19,95 iF FF tS (95%) = 50.5 ± (2.093)(1.00) = 50.5 ± 2.1 N (95%) Here F i denotes the value of any measurement of force, F. Column 2: 2 19,95 F Ft S (95%) = 50.7 ± 2.53 N (95%) N i i1 1 F 50.5 N FN = == 21 /2 1 1 [ ( ) ] 1.00 1 N Fi i SF F N N = =− =
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4-21 Column 3: 3 19,95 iF FF tS (95%) = 50.6 ± 2.11 N (95%) COMMENT The above probability statement reflects the scatter of the data set. In effect, it provides a range of values in which any measured value is expected to fall with 95% probability. A 95% probability with this statistical statement implies that at least 19 out of every 20 measurements are expected to fall in the range defined for F i . Indeed, inspection of the dataset shows that this is a true statement.
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4-22 PROBLEM 4.12 KNOWN: Data of Table 4.8, Column 1 N = 20 FIND: SOLUTION For this dataset in Column 1: with 11 9 N ν =−= . Then from Table 4.4, t 19,95 = 2.093. Then, we
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HW-3_solutions - PROBLEM 4.11 Data of Table 4.8, Column 1 N...

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