BUSINESS STATISTICS

Business Statistics

Business Statistics

Qestion 1

a) Target population

The target population is the entire group a researcher is interested in; the group about which the researcher wishes to draw conclusions.

Example

Suppose we take a group of men aged 35-40 who have suffered an initial heart attack. The purpose of this study could be to compare the effectiveness of two drug regimes for delaying or preventing further attacks. The target population here would be all men meeting the same general conditions as those actually included in the study.

Sample Frame

A sample frame is a list that includes every member of the population from which a sample is to be taken. Without some form of sample frame, a random sample of a population, other than an extremely small population, is impossible.

When a list of the population of interest is not available, an alternate method for capturing the population must be found. Most surveys carried out by governmental statistical agencies rely on a sample frame that is composed of maps that partition the entire country into enumeration areas. In that case, a multi-stage sample design is required. Enumeration areas are first randomly sampled, and then individual housing units are sampled from within the enumeration areas. Finally, individuals are sampled from within the housing units.

Even though the set of maps of enumeration areas is not a list of individuals in the population, it is still considered a sample frame. In that case, however, it is a sample frame of individuals that reside in housing units, not of the total population. Any individual who does not live in a housing unit, for example, a homeless person, is not covered by the sample frame.

Stratified Sampling

There may often be factors which divide up the population into sub-populations (groups / strata) and we may expect the measurement of interest to vary among the different sub-populations. This has to be accounted for when we select a sample from the population in order that we obtain a sample that is representative of the population. This is achieved by stratified sampling.

A stratified sample is obtained by taking samples from each stratum or sub-group of a population.

When we sample a population with several strata, we generally require that the proportion of each stratum in the sample should be the same as in the population.

Stratified sampling techniques are generally used when the population is heterogeneous, or dissimilar, where certain homogeneous, or similar, sub-populations can be isolated (strata). Simple random sampling is most appropriate when the entire population from which the sample is taken is homogeneous. Some reasons for using stratified sampling over simple random sampling are:

1. the cost per observation in the survey may be reduced;

2. estimates of the population parameters may be wanted for each sub-population;

3. increased accuracy at given cost.

Example

Suppose a farmer wishes to work out the average milk yield of each cow type in his herd which consists of Ayrshire, Friesian, Galloway and Jersey cows. He could divide up his herd into the four sub-groups and take samples from ...