SAMPLING DISTRIBUTION ASSIGNMENT HELP

The distribution of all possible values which can be assumed by some statistic, computed from samples of the same size randomly drawn from the same population is called the sampling distribution of that statistics. Sampling must be based on random selection to each one of the items in the universe. Only then, the representative character of sampling will be ensured.

Standard Error:

The standard deviation of a sampling distribution of a given statistics is frequently called the standard error of that statistics. The difference between the terms ‘standard deviation and standard error’ is that the former concerns original values, the latte concern the statistic computed from samples or original values.

Utility of the Standard Error:

The concept of standard error is of great significance in statistical studies because of the great significance in statistical studies because of the following reasons:

• Standard error is a useful instrument in the testing of a given hypothesis.
• It gives an idea about the unreliability of a sample. The greater is the standard error the greater will be the departure of actual distribution from the expected one. Thus greater the unreliability.
• It helps in determining the limits within which the parameter values are expected to lie.

Significance Testing:

A sampling investigation produces a result which has to be compared with the one expected on the basis of population parameter. Because of the laws of chance, it is possible that any particular sample may produce a result which is out of accord with the one expected. Before acting hastily or emotionally we must try to determine whether the difference is significant and cannot arise merely because of the use of sampling.

Lying Down of Hypothesis:

A statistical hypothesis, or simply a hypothesis, is a tentative conclusion logically drawn concerning any parameter of the population. All hypotheses may be verified on the basis of certain sample tests. The common way of stating a hypothesis is that there is no difference between two values, when population mean is compared with the sample mean. A statistical hypothesis which is stated for the purpose of possible acceptance is called null hypothesis.

Test Statistic:

The decision to accept null hypothesis or the alternate hypothesis is made on the basis of a statistics computed from the sample. Such a statistics is called the test statistic based on an appropriated probability distribution. These methods have the same fundamental procedure in testing the hypothesis.

Level of Significance:

The maximum probability of making a type-I error specified in a test of hypothesis is called the level of significance. The level of significance is usually specified before a test is made.

Critical Region:

The critical or rejection region is the region which corresponding to a pre-determined level of significance a. Whenever the sample statistic falls in the critical region, we reject the hypothesis as it will be considered to be probably false. The selection of decision rule is essentially a matter of the determine of the rejection region.

Two Tailed Tests and One-Tailed Test:

The critical region may be represented by a portion of the area under the normal curve in two ways:

• two tails or sides under the curve and
• one tails or side under the curve which is either the right tail or the left tail.

The tests of hypothesis which are based on the critical region represented by both tails under the normal curve are called two tailed or two sides tests. If the critical region is represented by one tail, the tests are called one tailed tests or one-sided tests.

Determination of a proper sample size:

The need for the determination of a proper size of the sample is very great of practical use in business where either the standard error is known on the basis of past experience or where a given absolute level of accuracy is desired. If the sample size is too large, more money and time have to be spent but the results may not be commensurate with it. Also, a valid conclusion may not be reached if the sample size is too small; therefore, the need for a proper size is given in the following two cases:

• Sample size for Estimating a population Mean
• Sample size for Estimating a population Proportion

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