A. They are equal to each other.
Add up each number and you get 19.53 for both groups then when you divide by 9 ( the amount of individuals in each group) you get 2.17 for both groups so the mean is the same.
Answer with explanation:
Given : Sample mean =![\overline{x}=\text{48.47 pounds}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%3D%5Ctext%7B48.47%20pounds%7D)
Standard deviation : ![\sigma=\text{ 3.1 pounds.}](https://tex.z-dn.net/?f=%5Csigma%3D%5Ctext%7B%203.1%20pounds.%7D)
Sample size : n = 36
Claim : ![\mu\neq50](https://tex.z-dn.net/?f=%5Cmu%5Cneq50)
∴ ![H_0:\mu=50](https://tex.z-dn.net/?f=H_0%3A%5Cmu%3D50)
![H_1:\mu\neq50](https://tex.z-dn.net/?f=H_1%3A%5Cmu%5Cneq50)
Since the alternative hypothesis is two tail , then the test is two tail test.
By using a z statistic and a 0.05 level of significance. Reject
if z < -1.960 or is z> 1.960.
Then , the test static for population mean is given by :-
![z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B%5Coverline%7Bx%7D-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
![z=\dfrac{48.47-50}{\dfrac{3.1}{\sqrt{36}}}\approx-2.96](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B48.47-50%7D%7B%5Cdfrac%7B3.1%7D%7B%5Csqrt%7B36%7D%7D%7D%5Capprox-2.96)
We reject
since
. We have statistically significant evidence at
to show that the mean amount of garbage per bin is not different from 50.
Answer:
You should get -20
Step-by-step explanation:
;)
Answer:
The percentage decrease is 29%
Step-by-step explanation:
Given
![Initial = 300](https://tex.z-dn.net/?f=Initial%20%3D%20300)
![Final = 213](https://tex.z-dn.net/?f=Final%20%3D%20213)
Required
Determine the percentage decrease
This is calculated as thus:
![\%Percentage = \frac{|Final - Initial |}{Initial} * 100\%](https://tex.z-dn.net/?f=%5C%25Percentage%20%3D%20%5Cfrac%7B%7CFinal%20-%20Initial%20%7C%7D%7BInitial%7D%20%2A%20100%5C%25)
Substitute values for Final and Initial
![\%Percentage = \frac{|213 - 300|}{300} * 100\%](https://tex.z-dn.net/?f=%5C%25Percentage%20%3D%20%5Cfrac%7B%7C213%20-%20300%7C%7D%7B300%7D%20%2A%20100%5C%25)
![\%Percentage = \frac{|-87|}{300} * 100\%](https://tex.z-dn.net/?f=%5C%25Percentage%20%3D%20%5Cfrac%7B%7C-87%7C%7D%7B300%7D%20%2A%20100%5C%25)
<em>Get absolute value of -87</em>
![\%Percentage = \frac{87}{300} * 100\%](https://tex.z-dn.net/?f=%5C%25Percentage%20%3D%20%5Cfrac%7B87%7D%7B300%7D%20%2A%20100%5C%25)
![\%Percentage = \frac{87* 100\%}{300}](https://tex.z-dn.net/?f=%5C%25Percentage%20%3D%20%5Cfrac%7B87%2A%20100%5C%25%7D%7B300%7D)
![\%Percentage = \frac{8700\%}{300}](https://tex.z-dn.net/?f=%5C%25Percentage%20%3D%20%5Cfrac%7B8700%5C%25%7D%7B300%7D)
![\%Percentage = 29\%](https://tex.z-dn.net/?f=%5C%25Percentage%20%3D%2029%5C%25)
Hence, the percentage decrease is 29%
Answer:
18 square units
Step-by-step explanation:
area = full square units + 1/2 x half- full square units
full square units = 12
half- full square units = 12
= 12 + (1/2 x 12)
=12 + 6
=18 square units