Define the target population and the sampling frame in each of the following situations:
A target population can be defines as all elements, objects, people, products, etc. researchers like to study about. In fact, target population possesses information the researcher is looking for. In other words, target population is the source of information sought by the researcher and from where the inferences have to be made.
Sampling frame is the fraction of a larger population that represents the elements of the target population. Some of the sampling frame could be the telephone directory, directory listing of the different organization in an industry, etc.
a. The manufacturer of a new cereal brand wants to conduct in home product usage tests in Chicago.
i. Target population: All families of the Chicago
ii. Sampling frame: census report about resident of Chicago
b. A national chain store wants to determine the shopping behavior of customers who have its store charger card.
i. Target population: All store customers or all store customers who have store charger card are possible target population.
ii. Sampling frame: Store record of customer who have charger card is the sampling frame.
c. A local TV station wants to determine households viewing habits and programming preferences.
i. Target population: all local families or household.
ii. Sampling frame: Local families guide or telephone directories
d. The local chapter of the American marketing association wants to test the effectiveness of its new member drive in Atlanta.
i. Target population: all new members of the American marketing association of Atlanta
ii. Sampling frame: Records managed by the American marketing association in Atlanta for its recent members.
2. A manufacturer would like to survey users to determine the demand potential for a new power press. The new press has a capacity of 500 tons and costs $225,000. It is used for forming products from lightweight and heavy weight steel and can be used by auto mobile, construction equipment and major appliance manufacturers.
a. Identify the population and sampling frame that could be used.
i. Target population: All automobile manufacturers, construction equipment manufacturers and appliance manufacturers.
ii. Sampling frame: An association directory listing of the individual manufacturer corporation of automobile industry, construction equipment industry and home appliances manufacturing industry.
b. Describe how a simple random sample can be drawn using the identified sampling frame.
Using simple random sampling method to draw sample size from the sampling frame is the easiest way of selecting sample size. In this method, the first job of the researcher is to assign a unique identification number to the each element of the sampling frame. The unique identification numbers which is assigned to the each element of the sampling frame is randomly generated either using computer routine or a statistical table. Using this method, sample is generated by a random procedure where all element of the sample frame has equal probability of being in the final sample size. Alternatively, a researcher can place all names of the sampling frame and then shake the container properly to reduce the bias and final sample list can be drawn out in an unbiased manner.
c. Could a stratified sample be used? If so how?
Yes, Stratified sample can also be used to draw a sample from the sampling frame. Actually this is the two step process where population is categorized or partitioned into various small populations which is called strata. Using this method, the researcher will try to place all similar or homogeneous element of the population in one stratum and different or heterogeneous elements in different strata.
In other words, in this sampling method, entire population of the sampling frame is divided into smaller groups of population commonly known as strata were strata are formed based on the specific attribute or characteristic of the elements of individual units of the entire population. And then a random sample from each stratum is taken, where percentage of the elements taken from each stratum depends upon the size of the stratums compared to the population.
The key of this method is that all elements should be assigned to only one strata and not a single element is omitted from assigning a particular strata wherever it fits the most. Finally, Simple random sampling method is used to draw sample from each stratum.
While using stratified sampling in above problem situation, we can divide all manufacturers’ auto, construction equipment and major appliances into homogenous strata. For example, we can divide auto manufacturers into different strata like car manufactures, truck manufacturers, motorbike manufacturers, etc and then we can select sample from each category of manufacturers to make sure that our sample represents all varieties of the larger population.
d. Could a cluster sample be used? If so how?
Yes, cluster sample can also be used to draw sampling from the identified sampling frame. Cluster sampling is the multi stage sampling in which sample of area is chosen in the first stage and sample of respondent will be selected from the each previously identified sample of area using simple random sampling method. Therefore, it is multistage sampling having at least two or more than two stage. Cluster sampling is popular because it reduces cost of research because researchers do not have to travel as he/she doesn’t need a sampling frame listing all the elements in the target population rather sampling cluster is determined by selecting respondent from certain areas only, or certain time-periods only.
In other words, in cluster sampling method all the naturally formatted groups (for example, auto manufacturers in Detroit, Michigan) are selected as samples in cluster sampling. One of the major advantages of cluster sampling is that it does not require sampling frames of all the sampling units. When the clusters are selected from the whole lot of population then, they are compiled into frames. And finally other statistical tools are used to draw conclusion out of those selected cluster.
To use cluster method in above example, we can determined the cluster of auto manufacturers by geographic location, for example auto manufacturers of Detroit, Michigan or construction equipments manufacturers in Columbus, Ohio and then use simple random sampling method to select respondent from each city for further analysis.
e. Which sampling technique would you recommend? Why?
Since we are determining the demand potential for a new power press we want high level of precision. Therefore, the best alternative sampling method is stratified sampling method. One of the major benefits of using this method is that this method ensures that all minority groups are adequately included in the final sample. The main reason for choosing this method is that it aims to minimize or eliminate standard error with some control over variance and this method will give statistically more accurate result than simple random sampling method and cluster sampling method.
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