Answer: B data gathering
Step-by-step explanation:
all of those examples are examples of gathering data
Answer:
Inverse property of addition is what I think.
Step-by-step explanation:
3(m + 2) - 4(2m - 9)
= 3m + 6 - 8m + 36
= 3m - 8m + 6 + 36 (now, we will group like terms).
= -5m + 42.
Answer:
The upper limit is
![k = 52.94](https://tex.z-dn.net/?f=k%20%3D%20%2052.94)
Step-by-step explanation:
From the question we told that
The sample size is ![n = 16](https://tex.z-dn.net/?f=n%20%3D%20%2016)
The sample mean is ![\= x = 50](https://tex.z-dn.net/?f=%5C%3D%20x%20%3D%20%2050)
The sample variance is ![\sigma ^2 = 36](https://tex.z-dn.net/?f=%5Csigma%20%5E2%20%20%3D%20%2036)
For a 95% confidence interval the confidence level is 95%
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
![\alpha = 100 - 95](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%20100%20-%2095)
![\alpha = 5 \%](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%205%20%5C%25)
![\alpha = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%200.05)
Next we obtain the critical value of
from the normal distribution table(reference- math dot armstrong dot edu), the value is
![Z_{\frac{ \alpha }{2} } = 1.96](https://tex.z-dn.net/?f=Z_%7B%5Cfrac%7B%20%5Calpha%20%7D%7B2%7D%20%7D%20%3D%20%201.96)
Generally the margin of error is mathematically represented as
![E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }](https://tex.z-dn.net/?f=E%20%3D%20%20Z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%20%2A%20%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%20%7D)
Here
is the standard deviation which is mathematically evaluated as
![\sigma = \sqrt{\sigma^2}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%20%5Csqrt%7B%5Csigma%5E2%7D)
substituting values
![\sigma = \sqrt{36}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%20%5Csqrt%7B36%7D)
=> ![\sigma = 6](https://tex.z-dn.net/?f=%5Csigma%20%3D%206)
So
![E = 2.94](https://tex.z-dn.net/?f=E%20%3D%202.94)
The 95% confidence interval is mathematically represented as
![\= x - E < \mu < \= x + E](https://tex.z-dn.net/?f=%5C%3D%20x%20%20-%20E%20%20%3C%20%20%5Cmu%20%3C%20%20%5C%3D%20x%20%20%2B%20E)
substituting values
![50 -2.94 < \mu](https://tex.z-dn.net/?f=50%20-2.94%20%20%20%3C%20%20%5Cmu%20%3C50%20%2B2.94)
![47.06 < \mu](https://tex.z-dn.net/?f=47.06%20%3C%20%20%5Cmu%20%3C52.94)
The upper limit is
![k = 52.94](https://tex.z-dn.net/?f=k%20%3D%20%2052.94)