# 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.

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## Question:

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.

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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:

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