Respuesta :
Complete question is;
On a given day, the proportion of workers from Company B who purchase a coffee from the company cafeteria is 0.62 and the proportion of workers from Company C who purchase a coffee from the company cafeteria is 0.71. A random sample of 40 workers was selected from Company B and another random sample of 40 workers was selected from Company C. The proportion of workers from Company B who purchased coffee was p^_B = 0.70 and the proportion of workers from Company C who purchased coffee was p^_C = 0.75.
What is the correct unit of measurement for the mean of the sampling distribution p^_B - p^_C?
A) Days
B) Dollars
C) Companies
D) Workers
E) There are no units associated with the mean of the sampling distribution
Answer:
E) There are no units associated with the mean of the sampling distribution
Step-by-step explanation:
We are given;
Population proportion for workers from Company B who purchase a coffee from the company cafeteria as 0.62
Population proportion for workers from Company C who purchase a coffee from the company cafeteria as 0.71
Now, we were told that a random sample of 40 each were selected from both company B & C and the sample proportion were;
p^_B = 0.70 and p^_C = 0.75
Now, this proportions don't have any units as it is based on a ratio of the number of people that purchased coffee to the number of people surveyed.
Thus we can conclude that p^_B - p^_C will not have any units associated with it.
The possible outcomes of the difference in proportions of the two samples
based on on the individual proportions are not associated with a unit.
- The correct option for the unit of measure of the sampling distribution [tex]\hat p_B - \hat p_C[/tex] is E. There are no units associated with the mean of the sampling distribution.
Reasons:
The given parameters are;
The proportion of workers of Company B who purchase coffee from the
Company B workers that purchase coffee from the cafeteria = 0.62
Company A workers that purchase coffee from the cafeteria = 0.71
Number of workers in the sample from Company B = 40
Number of workers in the sample from Company A = 40
Proportion of Company B workers who purchase coffee, [tex]\hat p_B[/tex] = 0.71
Proportion of Company C workers who purchase coffee, [tex]\hat p_C[/tex] = 0.75
Required:
The unit of the mean of the sampling distribution of [tex]\mathbf{\hat p_B - \hat p_C}[/tex]
Solution:
The proportion of the workers that purchase coffee is given by the ratio of the number of workers that purchase coffee to the number of workers in the sample.
Therefore;
[tex]\displaystyle \hat p = \mathbf{\frac{Coffee \ buying \ workers}{Total \ number \ of \ workers}}[/tex]
Given that the unit of the numerator and denominator are both workers,
that divide out, we have that the [tex]\mathbf{\hat p}[/tex], [tex]\mathbf{\hat p_B}[/tex], [tex]\mathbf{\hat p_C}[/tex] and therefore [tex]\hat p_B - \hat p_C[/tex] are not
associated with a unit.
Therefore;
The correct option is; E. There are no units associated with the mean of the sampling distribution.
Learn more here about sampling distribution of a sample proportion here:
https://brainly.com/question/14261491
