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Cluster Sample

By Author: peter
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Some populations exist or can be naturally divided into clusters or groups of basic units in the population. A cluster sample is obtained by picking at random some clusters from the entire list of clusters in the population and then picking some or all of the units from the selected clusters. As an example, suppose a retailer receives a shipment of 10, 000 cathode tubes in 1, 000 boxes, 10 tubes per box. Suppose the retailer decides to test fifty tubes to see if they meet the quality standards. A simple random sample would not be feasible in this situation unless all the boxes were opened. Cluster sampling is most suitable here if each box can be regarded as a natural cluster. The retailer could pick five boxes at random and test every tube in each of the by contradiction. For example, Omega Replica suppose a teacher strongly suspects that students coming from families at a higher economic level perform better than students at the lower level. This is what the teacher believes she can establish and so the burden of proof is on her. Under Ho we will say that this is not the case and stat.

Ho: Students at a higher economic level do not perform better. Against this null hypothesis we will give the alternative hypothesis as HA: Students at a higher economic level do perform better. Thus, it is the claim of the researcher that is stated as the alternative hypothesis. For this reason, the alternative hypothesis is sometimes referred to as the research hypothesis. The null hypothesis asserts, in essence, that there is no merit to the researcher's claim. If the sample evidence is such that it leads us to reject Ho, then we will, of course, accept HA.

At the heart of setting the two hypotheses this way is the question, "Do students coming from families at a higher economic level perform better than students at the lower level? " In the final analysis, the null hypothesis and the alternative hypothesis are determined by the question posed in the statement of the problem. Here are some additional examples.

• A businessman wonders: "Are the sales this year going to be better than last year?" Here we write the following.

Ho: The sales are not going to be better than last year. HA: The sales will be better than last year.

• An agronomist wants to know: "Does the new breeding method increase grain production?" We write the following.

H0: The new method does not increase grain production. The new method does increase gram production.

In each of the preceding examples, the null hypothesis denies the claim posed in the Tag Heuer Carrera Replica question, explaining in part the usage of the term null. Thus, it makes good sense to pose the question appropriately, depending upon what the researcher is interested in establishing.

When we wish to establish a statement about the population with evidence obtained from the sample, the negation of the statement is what we take as the null hypothesis H0. The statement itself constitutes the alternative hypothesis HA. A test of statistical hypothesis is a rule or procedure that leads to a decision to accept or reject the hypothesis when the experimental sample values are obtained. This rule, formulated before drawing the sample, is often referred to as a decision rule.

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