Higher Engineering Mathematics

582 STATISTICS AND PROBABILITY in the intervals: mean±1 standard deviation, mean±2 standard deviations, or mean±3 standard devia ...

SAMPLING AND ESTIMATION THEORIES 583 J Thus,the confidence limits of the mean of the population are: x± zcσ √ N √( Np−N Np− 1 ) ...

584 STATISTICS AND PROBABILITY Problem 6. The mean diameter of a long length of wire is to be determined. The diameter of the wi ...

SAMPLING AND ESTIMATION THEORIES 585 J (6) is used, i.e. the confidence limits of the estimated mean of the population areμx±zcσ ...

586 STATISTICS AND PROBABILITY the slings of this diameter produced by this company. [10.91 t to 11.27 t] The time taken to ass ...

SAMPLING AND ESTIMATION THEORIES 587 J Table 61.2 Percentile values (tp) for Student’stdistribution withνdegrees of freedom (sha ...

588 STATISTICS AND PROBABILITY This indicates that the actual diameter is likely to lie between 1.843 cm and 1.857 cm and that t ...

SAMPLING AND ESTIMATION THEORIES 589 J 10 samples of the materials. The mean and standard deviation of the results are found to ...

Statistics and probability 62 Significance testing 62.1 Hypotheses Industrial applications of statistics is often con- cerned wi ...

SIGNIFICANCE TESTING 591 J (ii) if the null hypothesis is rejected and the defect rate rises to 5% or over, stop the machine and ...

592 STATISTICS AND PROBABILITY Using Table 58.1 of partial areas under the stan- dardised normal curve given on page 561, az-val ...

SIGNIFICANCE TESTING 593 J and standard deviation are part of a normal distri- bution. For a set of results to be probably signi ...

594 STATISTICS AND PROBABILITY Table 62.1 Level of Significance,α 0.1 0.05 0.01 0.005 0.002 z-value, one-tailed test { −1.28 −1. ...

SIGNIFICANCE TESTING 595 J the expansion of (q+p)N, taken from the left. Thus: Number of Probability defective components 0 qN 1 ...

596 STATISTICS AND PROBABILITY 10% is (area to the left of mean−area between mean and az-value of−0.37), i.e. 0. 5 − 0. 1443 = 0 ...

SIGNIFICANCE TESTING 597 J Probability of no defective screws in a sample, qN= 0. 925 =0.0718 Probability of 1 defective screw i ...

598 STATISTICS AND PROBABILITY The particular value ofxof a large sample drawn for a significance test is therefore part of a no ...

SIGNIFICANCE TESTING 599 J For large samples, say, a minimum ofNbeing 30, the factor √( N N− 1 ) is √ 30 29 which is approximate ...

600 STATISTICS AND PROBABILITY Problem 5. The mean lifetime of a random sample of 50 similar torch bulbs drawn from a batch of 5 ...

SIGNIFICANCE TESTING 601 J The null hypothesis is that the sample and population means are equal, i.e.H 0 :x=μ. The alternative ...