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# Sampling and methods of doing sampling Assignment

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Sampling and methods of doing sampling Assignment

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### Sampling and methods of doing sampling Assignment

1. 1. Sampling and methods of doing sampling Basic Concepts Of Sampling With a single grain of rice, an Asian housewife tests if all the rice in the pot has boiled; from a cup of tea, a tea-taster determines the quality of the brand of tea; and a sample of moon rocks provides scientists with information on the origin of the moon. This process of testing some data based on a small sample is called sampling. Sampling is the process by which inference is made to the whole by examining a part. Purpose of Sampling The purpose of sampling is to provide various types of statistical information of a qualitative or quantitative nature about the whole by examining a few selected units. The sampling method is the scientific procedure of selecting those sampling units which would provide the required estimates with associated margins of uncertainty, arising from exam Methods of Sample Selection Simple Random Sampling In this method each item of the data (population) has the same probability of being selected in the sample. The selection is usually made with the help of random numbers. Suppose there are N=850 students in a school from which a sample of n=10 students is to be taken. The students are numbered from 1 to 850. Since our data runs into three digits we use random numbers that contain three digits. All numbers exceeding 850 are ignored because they do not correspond to any serial numbers in the data. In case the same number occurs again, the repetition is skipped.
2. 2. Systematic Sampling In this method first we have to number the data items from 1 to N. Suppose the sample size be n, then we have to calculate the sampling interval by dividing N by n. And generate a number between 1 and N/n and select that data item to be in the sample. Other items in the sample are obtained by adding the sampling interval N/n successively to the random number. Advantage of this method is that the sample is evenly distributed over the entire data. The town of Fairfax is divided up into N = 576 blocks which are numbered consecutively. A 10 percent sample of blocks is to be taken, which gives a sampling interval of k = 10. If the random number between 1 and 10 is 3, the blocks with the numbers 03, 13, 23, 33, 43... 573 are in the sample. Sampling with unequal probabilities When the data items vary considerably in size, a simple random or a systematic random sample of items does not produce a good estimate due to high variability. In such a situation we get a better estimate by giving higher probability of selection to the larger data items. Applications of sampling techniques Major TV networks rely on surveys to tell them how many and what types of people are watching their programs. The U.S. Bureau of Census conducts a survey every month to obtain information on employment and unemployment in the nation. Local housing authorities make surveys to ascertain satisfaction of people in public housing with their living accommodations. Local transportation authority’s conduct surveys to acquire information on people's commuting and travel habits. Magazines and trade journals utilize surveys to find out what their subscribers are reading. Surveys are used to ascertain what sorts of people use our national parks and other recreation facilities. Auto manufacturers use surveys to find out how satisfied people are with their cars.
3. 3. Advantages of Sampling Greater economy: The total cost of a sample will be much less than that of the whole lot. Shorter time-lag: With smaller number of observations it is possible to provide results much faster as compared to the total number of observations. Greater scope: Sampling has a greater scope regarding the variety of information by virtue of its flexibility and adaptability. Actual appraisal of reliability Limitations of sampling Errors due to sampling may be high for small administrative areas. Sampling may not be feasible for problems that require very high accuracy