Respuesta :
Answer:
B: Sampling without replacement will result in a standard deviation less than but close to √0.4(0.6)/500
.Step-by-step explanation:
answer on khan academy
Sampling without replacement will result in the standard deviation greater than but close to [tex]\sqrt{\dfrac{0.4(0.6)}{500}}[/tex] and this can be determined by using the standard deviation formula.
Given :
- At a large corporation, 6,000 employees from department A and 4,000 employees from department B are attending a training session.
- A random sample of 500 employees attending the session will be selected.
- Consider two sampling methods: with replacement and without replacement.
1) With Replacement --
The standard deviation is given by the formula:
[tex]\rm \hat{p}=\sqrt{\dfrac{p(1-p)}{n}}[/tex] ---- (1)
where the value of 'p' is given by:
[tex]\rm p=\dfrac{4000}{10000}=0.4[/tex]
Now, substitute the value of p and n in the equation (1).
[tex]\rm \hat{p}=\sqrt{\dfrac{0.4(1-0.4)}{500}}[/tex]
[tex]\rm \hat{p}=\sqrt{\dfrac{0.4(0.6)}{500}}=0.02190[/tex]
2) Without Replacement --
The standard deviation is given by the formula:
[tex]\rm \hat{p}=\sqrt{\dfrac{p(1-p)}{n}\times \left(1-\dfrac{n-1}{N-1}\right)}[/tex] ---- (2)
where the value 'p' is given by:
[tex]\rm p=\dfrac{4000}{10000}=0.4[/tex]
Now, substitute the value of p, n, and N in equation (2).
[tex]\rm \hat{p}=\sqrt{\dfrac{0.4(1-0.4)}{500}\times \left(1-\dfrac{500-1}{10000-1}\right)}[/tex]
Simplify the above expression.
[tex]\rm \hat{p} = 0.1442[/tex]
So, from the above calculation, the correct option is C) Sampling without replacement will result in the standard deviation greater than but close to [tex]\sqrt{\dfrac{0.4(0.6)}{500}}[/tex].
For more information, refer to the link given below:
https://brainly.com/question/23044118
