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Ainat [17]
3 years ago
5

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.
Mathematics
1 answer:
jok3333 [9.3K]3 years ago
4 0

Answer:

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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Determine the sum of the arithmetic series: 5+18 +31 +44 + ... 161.
Finger [1]

Answer:

1079

Step-by-step explanation:

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18-5 = 13

31-18=13

44-31=13

161=5+13*12

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\displaystyle \sum_{k=0}^{k=12} \ {(5+13k)}\\\\=\sum_{k=0}^{k=12} \ {(5)} + 13\sum_{k=1}^{k=12} \ {(k)}\\\\=13*5+13*\dfrac{12*13}{2}\\\\=65+13*13*6\\\\=65+1014\\\\=1079

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2 Construct a rational function that will help solve the problem. Then, use a calculator to answer the question.
vaieri [72.5K]

Answer:

<u><em>Dimension of box:-</em></u>

Side of square base = 10 in

Height of box = 5 in

Minimum Surface area, S = 300 in²

Step-by-step explanation:

An open box with a square base is to have a volume of 500 cubic inches.

Let side of the base be x and height of the box is y

Volume of box = area of base × height

                 500=x^2y

Therefore, y=\dfrac{500}{x^2}

It is open box. The surface area of box, S .

S=x^2+4xy

Put  y=\dfrac{500}{x^2}

S(x)=x^2+\dfrac{2000}{x}

This would be rational function of surface area.

For maximum/minimum to differentiate S(x)

S'(x)=2x-\dfrac{2000}{x^2}

For critical point, S'(x)=0

2x-\dfrac{2000}{x^2}=0

x^3=1000

x=10

Put x = 10 into y=\dfrac{500}{x^2}

y = 5

Double derivative of S(x)

S''(x)=2+\dfrac{4000}{x^3} at x = 10

S''(10) > 0

Therefore, Surface is minimum at x = 10 inches

Minimum Surface area, S = 300 in²

7 0
3 years ago
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