A large retail company has 500 stores in the United Sates and 300 stores in Europe. The average number of employees per store is 200, for a total of 100,000 employees in the United States and 60,000 employees in Europe. The company is considering offering employees one of two new benefits --one additional day of paid vacation per year or a small increase in pay. A survey will be given to a sample of employees to investigate which benefit is preferred and whether there is a difference in preference between employees in the United States and employees in Europe. Two sampling methods have been proposed. The Company will randomly select 8 stores from its 800 stores. All employees at the 8 selected stores will be asked which bandit they prefer. The company will randomly select 1,000 employees from a list of all employees at the United States stores and 600 employees form a list of all employees at the European stores. All 1, 600 selected employees will be asked which benefit they prefer.

A) One of the two methods results in a stratified sample of employees and the other results in a cluster sample of employees.

i) Identify the sampling method that results in a stratified sample employees and identify the strata.
ii) Identify the sampling method that results in a cluster sample of employees, and identify the clusters.

B) Give one statistical advantage and one statistical disadvantage of using sampling method 1.

A1)

Stratified sampling: Here, sampling is performed on element within each stratum( the European store and the United States store. Therefore, The technique of randomly selecting 1,000 employees from a list of all employees at the United States stores and 600 employees form a list of all employees at the European stores is a stratified sampling.

A 11)

Cluster sampling :

It involves dividing total population into groups, which should be a representation of the total population and each identified cluster is treated as a sampling unit, by randomly selecting 8 stores from 800, we have chosen 8 clusters, and all samples in the 8 clusters being sampled signals a single stage cluster design.

B) Advantage : stratified sampling usually saves cost as it encourages a small subset of the population while also encougung representativeness.

Disadvantage : It requires that the experimenter has prior knowledge of the population before being able to group into stratums

Step-by-step explanation:

A. i.) Proposed Sampling Method 2 that resulted in creating of strata where samples of the study was drawn from is: Stratified Random Sampling.

The strata are: employees from European stores and United State stores

ii.) Proposed Sampling Method 1 that resulted in creating of clusters from which samples are randomly selected from is: Cluster Sampling

The clusters are: the 8 stores randomly selected

B. Statistical Advantage of Using Proposed Sampling Method 1 (Cluster Sampling):

Statistical Disadvantages of Using Proposed Sampling Method 1 (Cluster Sampling):

The two sampling methods used will be described briefly:

Stratified Random Sampling: this method involves dividing the entire population that is being studied into homogenous groups which we can refer to as strata.

Cluster Sampling: this method of sampling involves dividing an entire population into different groups which we refer to as clusters. Thereafter, using a simple random method, clusters will be selected to use as sample for the study. All members in the clusters are then surveyed.

Therefore:

A. i.) Proposed Sampling Method 2 that resulted in creating of strata where samples of the study was drawn from is: Stratified Random Sampling.

The strata are: employees from European stores and United State stores

ii.) Proposed Sampling Method 1 that resulted in creating of clusters from which samples are randomly selected from is: Cluster Sampling

The clusters are: the 8 stores randomly selected

B. Statistical Advantage of Using Proposed Sampling Method 1 (Cluster Sampling):

Statistical Disadvantages of Using Proposed Sampling Method 1 (Cluster Sampling):

Learn more about Sampling Techniques here:

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step-by-step explanation:

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step-by-step explanation: