Identify the population
Statistics has two broad categories – descriptive and inferential statistics. In inferential statistics, random data is collected and used to draw suggestions about a specified population. To this end, populations form an essential basis in inferential statistics. Primarily, populations refer to a set of items or individuals under consideration during a statistical study. Populations can either be finite or infinite. Finite populations are those which comprise of objects or individuals that are countable while infinite populations contain uncountable elements. For instance, the population of a country is infinite as the total number of residence can be counted.
In most cases, infinite populations are mostly theoretical owing to their infinite sizes. It is important to note that the phenomenon under study plays a vital role in determining the population to be considered in evaluating a given aspect. The analysis of quality improvement is an example of an infinite population as applied to inferential statistics. In the case study, Top Films of All Time , the American Film Institute conducted a survey to find the top 100 favorite movies; the population consisted of the entire American movie lovers, critics, historians, and artists.
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Identify the sample
In statistics, populations are hard to work with owing to their size. With this in mind, a representative proportion of specific populations are used in statistics from which inferences can be drawn to arrive at inferred patterns for the population in question. Primarily, samples provide a logical and practical parameter from which conclusions for a given population may be drawn. It is important to note that samples are selected from a group of items or individuals who participate in a given survey or study. Additionally, for the inferences drawn from selected samples to be deemed credible, samples must be chosen randomly to ensure that each member of the intended population has an equal opportunity of being represented.
Practically, the choice of any sample in statistics should ensure that all elements in the population have a fair chance of being included in the sample. Besides, the choice of the items for the sample should be such that the selection of one element does not affect the chances of any other element from the population being chosen. In any research study, samples selected must be of sufficient size. This ensures that the inferences drawn from the sample represent the broader spectrum inherent to the population and warrant statistical analysis.
Most importantly, the size and type of population, as well as the phenomenon under study, are import factors in determining the sample to be used in any given research. For the case study, Top Films of All Time , the sample chosen comprised of 1500 film artists, critics, and historians. In essence, this sample was selected to represent the fraction of the American population who loved movies.
Is the sample representative of the population of all U.S. moviegoers? Explain your answer.
The selected sample for the case study did not represent the population of all U.S. moviegoers. First, the sample was skewed as it only considered film artists, critics, and historians. In practice, other stakeholders in the movie industry, such as movie fans, directors, producers, media houses, and other players in the entertainment sector, were not incorporated in the sampling procedure. To this end, the data emanated is not statistically sufficient as a basis from which inferences for the general American movie lovers could be drawn.
For the data obtained in this study to have inferred on the views of the total American population, random sampling would have been applied in the selection of participants. In totality, the sample drawn from only a section of the total population yield data that does not reflect the overall opinion of the American population in this case study. In essence, the deficiencies in the provision of inferred data from the sample stem from the lack of sufficient and direct mapping of some elements in the sample chosen to those in the population under investigation. The lack of direct mapping of elements in the population to the samples is a recipe for variations in the data collected. The differences emerging affect the reliability of collected data and consequently affecting the overall inference of this data to reflect on the opinion of the population.
Secondly, the sample size of 1500 out of the total population of the United States was not sufficient to represent the opinions of the total population. In practice, systematic random sampling, stratified sampling, cluster sampling, or multistage sampling would have sufficed in this case study. The use of either of the sampling techniques would have yielded a sample size from which the data collected would have been an apt representation or the general population in question. Based on the above facts, it is evident that the sample chosen for this case study does not reflect the population of all U.S. movie fans.
