Sampling
Sampling and tests of significance are very important tools in business economics. In fact one cannot do any meaningful marketing research without the requisite knowledge of sampling techniques.
Any collection (usually large) of individuals or objects is called a population or universe.
A finite subset of a population is called a sample. The number of individuals in a sample is called the sample size.
1. Random Sampling: When a sample is taken in such a way that each member of the population has the same probability of being selected, the sample so obtained is called a random sample and the technique is called random sampling.
2. Simple Sampling: It is a special case of random in which each event has the same probability of success and the probability of an event is independent of the success or failure of event in the preceding trails. Thus, simple sampling is a random sampling in which the trails are independent and the probability of success is constant.
3. Large and the small sample: Sample of size n > 30 is called large samples and samples of size n ≤ 30 is called small samples.
4. Hypothesis: In order to make certain decisions about a population on the basis of sample information, some assumption is made about the population. Such assumption, which are not necessarily true, are called statistical hypothesis.
5. Null Hypothesis: The hypothesis tested for possible rejection under the assumption that it is true, is called the null hypothesis.
6. Parameters and Statistics: The Statical constants of the population viz., mean (μ), variance (σ^{2}), etc., are usually referred to as parametrs. The statistical measures computed from the sample observations above, e.g., mean , variance (s^{2}), etc., are called statistics.
7. Level of significance : We are not introducing binomial statement and Normal distribution in this introductory book .The following statements may be taken as given:
(i) Normal distribution is the limiting case of the binomial distribution. When (i.e., the number of trials is indefinitely large) and neither P nor q is very small.
(ii) The vitiate Z is defined by
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