Respuesta :
Answer:
Part A:
n=196.66≅197 employees
Part B:
n=503.45≅503 employees
Step-by-step explanation:
Part A:
The formula we are going to use to find a sample size is gien below::
[tex]n=\frac{Z^2*S^2}{E^2}[/tex]
Where:
n is the sample size
Z is the distribution
S is the standard deviation
E is the margin
S=341, E=40
Z is calculated as:
Alpha=1-0.90
Alpha=0.1
Alpha/2=0.1/2
Alpha/2=0.05
From Standard distribution table Z at Alpha/2 is 1.645
[tex]n=\frac{1.645^2*341^2}{40^2}[/tex]
n=196.66≅197 employees
Part B:
S=341, E=25, Z=1.645
[tex]n=\frac{1.645^2*341^2}{25^2}[/tex]
n=503.45≅503 employees
The sample should be 197 and the management wants to be correct employees need to be selected is 503.
What is a z-score?
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
A survey is planned to determine the mean annual family medical expenses of employees of a large company.
The management of the company wishes to be 90% confident that the sample mean is correct to within plus or minus $40 of the population mean annual family medical expenses.
A previous study indicates that the standard deviation is approximately $341.
A. We know the formula
[tex]\rm n = \dfrac{Z^2 + S^2 }{E^2}[/tex]
where
n = sample size
Z = distribution
S = standard deviation
E = margin
Here
S = 341
E = 40
Z will be
[tex]\alpha =1-0.90\\\\\alpha =0.1\\\\\dfrac{\alpha }{2} = \dfrac{0.1}{2}\\\\\dfrac{\alpha }{2} = 0.05[/tex]
Then we have
[tex]\rm n = \dfrac{1.645^2+341^2}{40^2}\\\\\\n = 196.66 \approx 197[/tex]
B. For S = 341, E = 25, and Z = 1.645
[tex]\rm n = \dfrac{1.645^2+341^2}{25^2}\\\\\\n = 503.45 \approx 503[/tex]
More about the z-score link is given below.
https://brainly.com/question/13299273
