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CEE 110 PS7 and PS8 11 Examples

# CEE 110 PS7 and PS8 11 Examples - UNIVERSITY OF CALIFORNIA...

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UNIVERSITY OF CALIFORNIA, LOS ANGELES Civil and Environmental Engineering Department CEE 110 Introduction to Probability and Statistics for Engineers Spring Quarter 2011 MW 12-2 PM Franz 1178 Prof. K. D. Stolzenbach 5732J Boelter Hall, 206-7624 Problem Set 7 and 8 Examples _____________________________________________________________________________ 1. [ χ 2 = 10.829; P = 0.0286] 2. [b) 0.1151, 0.4207; c) 0.2578; d) 0.4364; e) 618]

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3. [r = -0.8028] 4. [0.6021; 12.177, 6.923, 19.10; y = 0.298 + 0.00837 x ; 0.633 mm; 24.1 ° C]
5. [0.75269; 0.696, 0.810; 0.0526] 6. Specifications for the diameter of a roller are 2.10-2.11 cm. Rollers that are too thick can be reground, while those that are too thin must be scrapped. Three machinists grind these rollers. Samples of rollers were collected from each machinist, and their diameters were measured. The results are as follows: Machinist Good Regrind Scrap Total A 328 58 14 400 B 231 48 21 300 C 409 73 18 500 Total 968 179 53 1200 Can you conclude that the proportions of rollers in the three categories differ among the machinists? a) State the appropriate null hypothesis b) Compute the expected values under the null hypothesis c) Compute the value of the chi-square statistic d) Find the p-value. What do you conclude?

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