The underlying principle of all statistical inference is one uses sample data to
ID: 3048344 • Letter: T
Question
The underlying principle of all statistical inference is one uses sample data to learn something ( that is to infer) about a population parameter. Convince me that you understand this statement by writing a short paragraph describing a statistical problem in which you use a sample statistic to infer something about a population parameter. Clearly, describe the problem where you utilize hypothetical numbers to explain the statistical inference process. Clearly identify and define the following terms in developing your example: parameter, population, sample, sample estimate, sampling error, and statistical inference. Be specific as possible.
Explanation / Answer
It is almost impossible to check each and every unit under study as it is time consuming and cost oriented process. Hence, we would have to draw few samples from the population and then examine and make claims about the overall population. For example, if we want to examine the average weight of females aged between 30-35 in the United States, it is almost impossible to survey each and every women in the United States aged between 30-35 and record their weights. Hence, we would choose few units amongst the population and then examine their weights and make a statement about the weights of women aged 30-35 in the United States. Lets suppose, the sample average weight is 143.3 lbs. Parameter refers to the numerical characteristic of the population from where the samples are taken. Population refers to the unit under study. Here, it is weights of women aged 30-35. Sample refers to the sample units taken from population (women aged 30-35). Sample estimate is the value derived from statistical analysis on the sample (here, it would be the 143.3 lbs). Sampling error is the error caused because of the difference of the sample and population estimates. Lets assume that the actual average weight of all the women aged 30-35 in the United States is 140 lbs, then the sampling error is 3.3 lbs. Finally, statistical inference means when we infer about the characteristics of population based on the estimates derived from the sample.
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