Please summarize the following information. !!!!

For much business analysis, successfully conducting a census is virtually impossible and the sample is a feasible alternative. Other reasons for sampling include cost reduction, potential for broadening the scope and time of the study, and loss reduction when the testing process destroys the product.

To take a sample, a population must be identified. Often the analyst cannot obtain an exact roster or list of the population and so must find some way to identify the population as closely as possible. The final list or directory used to represent the population and from which the sample is drawn is called the frame.

The two main types of sampling are random and nonrandom. Random sampling occurs when each unit of the population has the same probability of being selected for the sample. Nonrandom sampling is any sampling that is not random. The four main types of random sampling discussed are simple random sampling, stratified sampling, systematic sampling, and cluster or area sampling.

In simple random sampling, every unit of the population is numbered. A table of random numbers or a random number generator is used to selectnunits from the population for the sample.

Stratified random sampling uses the analyst's prior knowledge of the population to stratify the population into subgroups. Each subgroup is internally homogeneous but different from the others. Stratified random sampling is an attempt to reduce sampling error and ensure that at least some of each of the subgroups appears in the sample. After the strata are identified, units can be sampled randomly from each stratum. If the proportions of units selected from each subgroup for the sample are the same as the proportions of the subgroups in the population, the process is called proportionate stratified sampling. If not, it is called disproportionate stratified sampling.

With systematic sampling, everykth item of the population is sampled untilnunits have been selected. Systematic sampling is used because of its convenience and ease of administration.

Cluster or area sampling involves subdividing the population into nonoverlapping clusters or areas. Each cluster or area is a microcosm of the population and is usually heterogeneous within. A sample of clusters is randomly selected from the population. Individual units are then selected randomly from the clusters or areas to get the final sample. Cluster or area sampling is usually done to reduce costs. If a set of second clusters or areas is selected from the first set, the method is called two-stage sampling.

Four types of nonrandom sampling were discussed: convenience, judgment, quota, and snowball. Inconvenience sampling, the researcher selects units from the population to be in the sample for convenience. In judgment sampling, units are selected according to the judgment of the researcher. Quota sampling is similar to stratified sampling, with the researcher identifying subclasses or strata. However, the researcher selects units from each stratum by some nonrandom technique until a specified quota from each stratum is filled. With snowball sampling, the researcher obtains additional sample members by asking current sample members for referral information.

Sampling error occurs when the sample does not represent the population. With random sampling, sampling error occurs by chance. Nonsampling errors are all other research and analysis errors that occur in a study. They can include recording errors, input errors, missing data, and incorrect definitions of the frame.

According to the central limit theorem, if a population is normally distributed, the sample means for samples taken from that population also are normally distributed regardless of sample size. The central limit theorem also says that if the sample sizes are large the sample mean is approximately normally distributed regardless of the distribution shape of the population. This theorem is extremely useful because it enables analysts to analyze sample data by using the normal distribution for virtually any type of study in which means are an appropriate statistic, as long as the sample size is large enough. The central limit theorem states that sample proportions are normally distributed for large sample sizes.