## Honors Projects and Presentations: Undergraduate

Sampling

4-30-2010

Thesis

#### Degree Name

Bachelor of Science (BS)

#### Department

Mathematics, Physics and Statistics

#### Abstract

Data have become extremely important in the world today. Information is everywhere, and people are working to use it to their advantage, whether in business, politics, or science. For instance, political polls and market research surveys look to gain information about the people that they are serving. The amount of data that can be collected is incomprehensible. It is impossible to analyze all of the information that exists. That is where sampling comes into play. Sampling allows a researcher to select a part of a population to observe so that one may infer something about the whole population. It allows one to take the deluge of data and filter it down to a manageable amount by sampling. The sample design determines the quantity of information that is needed to estimate the population parameter of interest. (Scheaffer, Mendenhall, & Ott, 7) Also, since collecting data costs money, sampling tries to minimize costs, while maximizing the information from the sample. This implies a minimization of the variability. There is uncertainty that occurs in a sample since only a portion of the population is included. Sampling designs try to control and minimize the level of that uncertainty (i.e. variability). Then one can use the sample to make inferences about the larger population with a specified level of confidence. Sampling can be thought of as similar to experimental design. The main difference is that experimental design controls for factors and adjusts a certain variable for each group to compare. Sampling is simply an observation of something as it naturally occurs. There are no adjustments made to different groups. For example, a sample is conducted to estimate the deer population in two counties. Then the deer are observed according to the sampling design and the totals are calculated. It is an observation of how things are at the time of the survey. In an experimental design setting, a researcher would control what each observation would be. If one was interested in comparing fertilizers, the same type of seeds would be planted in the same soil 4 and the only thing that would change between observations would be the type of fertilizer. The experimenter controls exactly what information is to be provided. In the sampling setting, the information provided depends on the observation selected, instead of how the researcher constructed the experiment.

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