Test of hypotheses

Given a series of tests with the new material, the average yield x would be compared with Po. If x < Po, the new supplier would be dismissed. If X > Po, the question would be Is it sufficiently greater in the light of its corresponding reliability, i.e., beyond a reasonable doubt If the confidence intei v for p included Po, the answer would be no, but if it did not include Po, the answer would be yes. In this simple apphcation, the formal test of hypothesis would result in the same conclusion as that derived from the confidence intei val. However, the utility of tests of hypothesis lies in their generality, whereas confidence intei vals are restricted to a few special cases. 

A 7-day test was carried out, and daily yields averaged 91.6 percent with a sample standard deviations = 3.6 (this is not needed for the test of hypothesis). 

Test of Hypothesis for Matched Pairs Procedure Nomenclature... 

Test of Hypothesis Under the null hypothesis, the classification criteria are assumed to be independent, i.e.,... 

Suppose we have two methods of preparing some product and we wish to see which treatment is best. When there are only two treatments, then the sampling analysis discussed in the section Two-Population Test of Hypothesis for Means can be used to deduce if the means of the two treatments differ significantly. When there are more treatments, the analysis is more detailed. Suppose the experimental results are arranged as shown in the table several measurements for each treatment. The goal is to see if the treatments differ significantly from each other that is, whether their means are different when the samples have the same variance. The hypothesis is that the treatments are all the same, and the null hypothesis is that they are different. The statistical validity of the hypothesis is determined by an analysis of variance. 

From a modeling standpoint statisticians would define this problem as a two-population test of hypothesis. They would define the respective sample sheets as two populations from which 10 sample thickness determinations were measured for each. 

In the ultimate test of hypothesis c, Decodon plants were treated with (jR5 )-[6,2-14C2]- and (RS)-[6-3H,2 -14C]pclletierme to yield inactive alkaloids, whereas in concurrent experiments labeled decodine and decinine were obtained from other substrates. The accumulated evidence favored hypothesis e (see Scheme 4). 

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