Answer: ![t= -2.5](https://tex.z-dn.net/?f=t%3D%20-2.5)
Step-by-step explanation:
By considering the given statements :
Null hypothesis : ![\mu=10](https://tex.z-dn.net/?f=%5Cmu%3D10)
Alternative hypothesis :
( opposite of null hypothesis.)
As per given , we have
Sample size : n= 100
Sample mean : ![\overline{x}=9.75](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%3D9.75)
Sample standard deviations : ![s=1](https://tex.z-dn.net/?f=s%3D1)
Since population standard deviation is unknown , so we will perform t-test.
Formula for test statistic ( for population mean):
![t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}\\\\=\dfrac{9.75-10}{\dfrac{1}{\sqrt{100}}}\\\\=\dfrac{-0.25}{\dfrac{1}{10}}=-0.25\times10=-2.5](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7B%5Coverline%7Bx%7D-%5Cmu%7D%7B%5Cdfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%7D%5C%5C%5C%5C%3D%5Cdfrac%7B9.75-10%7D%7B%5Cdfrac%7B1%7D%7B%5Csqrt%7B100%7D%7D%7D%5C%5C%5C%5C%3D%5Cdfrac%7B-0.25%7D%7B%5Cdfrac%7B1%7D%7B10%7D%7D%3D-0.25%5Ctimes10%3D-2.5)
Hence, the required test statistic : ![t= -2.5](https://tex.z-dn.net/?f=t%3D%20-2.5)
F(x) = x^2 - 8x + 5
f(-1) = -1^2 - 8(-1) + 5
f(-1) = 1 + 8 + 5
f(-1) = 14 <==
This is one half of a simultaneous equation. Without the other half, the values are theoretically unsolvable.
With that said, with trial and error you can work this out. I came out with an answer of x=1, y=12.
This is not a good practice. It's time consuming to solve simultaneous questions like this. Make sure you use the other half of the equation in the future.
I hope this helps!
The size of the sample should be obtained at 2401 in order to be 95% confident
Given that:
Margi of error, ![ME=0.02](https://tex.z-dn.net/?f=ME%3D0.02)
Population proportion, ![p=0.50](https://tex.z-dn.net/?f=p%3D0.50)
To Find: The size of the sample that should be obtained in order to be 95% confident
Let the size of the sample be n
Using formula,
![n=(p*(1-p))*(z(0.05/2)/ME)^{2} \\n=(0.5*(1-0.5))*(1.96/0.02)^{2} \\n=0.25*9604\\n=2401](https://tex.z-dn.net/?f=n%3D%28p%2A%281-p%29%29%2A%28z%280.05%2F2%29%2FME%29%5E%7B2%7D%20%5C%5Cn%3D%280.5%2A%281-0.5%29%29%2A%281.96%2F0.02%29%5E%7B2%7D%20%5C%5Cn%3D0.25%2A9604%5C%5Cn%3D2401)
Therefore, the size of the sample should be obtained at 2401 in order to be 95% confident
Learn more about Population proportion here brainly.com/question/15703406
#SPJ4