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In: Statistics and Probability

Explain in your own words the three ideas of sample size. What are the differences between...

Explain in your own words the three ideas of sample size. What are the differences between that and a census?

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Expert Solution

Explain in your own words the three ideas of sample size?

The most frequently asked question concerning sampling is, "What size sample do I need?"

In addition to the purpose of the study and population size, three criteria usually will need to be specified to determine the appropriate sample size: the level of precision, the level of confidence or risk, and the degree of variability in the attributes.

The Level Of Precision:-

The level of precision, sometimes called sampling error, is the range in which the true value of the population is estimated to be. This range is often expressed in percentage points, (e.g., ±5 percent).

Example:- If a researcher finds that 60% of farmers in the sample have adopted a recommended practice with a precision rate of ±5%, then he or she can conclude that between 55% and 65% of farmers in the population have adopted the practice.

The Confidence Level:-

The confidence interval is the statistical measure of the number of times out of 100 that results can be expected to be within a specified range.

For example, a confidence interval of 90% means that results of an action will probably meet expectations 90% of the time.

The basic idea described in Central Limit Theorem is that when a population is repeatedly sampled, the average value of an attribute obtained is equal to the true population value.

In other words, if a confidence interval is 95%, it means 95 out of 100 samples will have the true population value within range of precision.

Degree Of Variability:-

Depending upon the target population and attributes under consideration, the degree of variability varies considerably. The more heterogeneous a population is, the larger the sample size is required to get an optimum level of precision. The less variable (more homogeneous) a population, the smaller the sample size.

A proportion of 50% indicates a greater level of variability than either 20% or 80%. This is because 20% and 80% indicate that a large majority do not or do, respectively, have the attribute of interest. Because a proportion of 0.5 indicates the maximum variability in a population, it is often used in determining a more conservative sample size, that is, the sample size may be larger than if the true variability of the population attribute were used.

Basis of difference Census Method Sample Method
1. Items to be studied

Under census method each & every unit of universe is studied.

Under sample method, only some of the items which represent the population are studied.
2. Suitability This method is suitable when the area of investigation is relatively small. This method is suitable where area of investigation is wide.
3. Conclusion In this method,conclusions are drawn on the basis of whole universe. In this method,conclusions are drawn on the basis of sample.
4. Time It is more time consuming method. It is less time consuming method.
5. Verification Under census method the results of investigation is not possible. Under sampling method results can be verified by taking out another sample.
6. Nature of method. It is an old method of investigation. It is new and practicable method.
7. Number of enumerators. Census method requires large number of enumerators. It does not require large number of enumerators.
8. Expensive It is more expensive. It is comparatively less expensive.

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