Higher Engineering Mathematics

602 STATISTICS AND PROBABILITY Breaking strength Frequency (kN) 9.8 1 10 1 10.1 4 10.2 5 10.5 3 10.7 2 10.8 2 10.9 1 11.0 1 Test ...

SIGNIFICANCE TESTING 603 J degrees of freedom in Student’st-distribution tables becomes 2 andνis given by (N 1 +N 2 −2). With th ...

604 STATISTICS AND PROBABILITY N 2 =50. Hence, equation (9) can be used to deter- mine thez-value of the difference of the sampl ...

SIGNIFICANCE TESTING 605 J of the difference of the means is within the range ±1.81, there isno significant difference between t ...

606 STATISTICS AND PROBABILITY a level of significance of 0.01.( Bessel’s correction isσˆ^2 = s^2 N N− 1 ). ⎡ ⎢ ⎢ ⎢ ⎣ x 1 = 23 . ...

J Statistics and probability 63 Chi-square and distribution-free tests 63.1 Chi-square values The significance tests introduced ...

608 STATISTICS AND PROBABILITY Face Observed Expected frequency frequency 149 40 235 40 332 40 446 40 549 40 629 40 Determine th ...

CHI-SQUARE AND DISTRIBUTION-FREE TESTS 609 J Table 63.1 Chi-square distribution χp^2 Percentile values (χ^2 p) for the Chi-squar ...

610 STATISTICS AND PROBABILITY Number of Observed Expected boys (B) frequency, frequency, and girls (G) oe 5B, 0G 11 6 4B, 1G 35 ...

CHI-SQUARE AND DISTRIBUTION-FREE TESTS 611 J o−e (o−e)^2 (o−e)^2 e 1 1 0.0250 5 25 0.3906 − 8 64 1.2308 − 1 1 0.0357 1 1 0.0909 ...

612 STATISTICS AND PROBABILITY Table 63.2 12 3 456 Class Class z-value for Area from Area for Expected mid-point boundaries,x cl ...

CHI-SQUARE AND DISTRIBUTION-FREE TESTS 613 J The data given below refers to the num- ber of people injured in a city by acciden ...

614 STATISTICS AND PROBABILITY with such distributions are calleddistribution-free tests; since they do not involve the use of p ...

CHI-SQUARE AND DISTRIBUTION-FREE TESTS 615 J Problem 5. A manager of a manufacturer is concerned about suspected slow progress i ...

616 STATISTICS AND PROBABILITY each as shown below: (A−B) + 1. 1 − 0. 9 + 1. 7 + 0. 8 − 0. 5 + 0. 4 − 0. 5 − 0. 1 + 0. 4 − 1. 6 ...

CHI-SQUARE AND DISTRIBUTION-FREE TESTS 617 J Table 63.4 Critical values for the Wilcoxon signed-rank test α 1 =5% 212 %1%^12 % α ...

618 STATISTICS AND PROBABILITY (iii) Taking the difference between the time taken for each order and 7 h gives: − 214 h + 234 h ...

CHI-SQUARE AND DISTRIBUTION-FREE TESTS 619 J hypothesis is accepted, i.e. the average oper- ating time is not significantly diff ...

620 STATISTICS AND PROBABILITY At a level of significance of 5%, use the Wilcoxon signed-rank test to test the null hypothesis t ...

CHI-SQUARE AND DISTRIBUTION-FREE TESTS 621 J (ii) Level of significanceα 1 =1%. (iii) Let the sizes of the samples benPandnQ, wh ...