Answer:
4
Step-by-step explanation:
Root32= 4×root2
Root32 is 4 times greater than root2
Pls mark as brainliest
Complete Question
Express the confidence interval 0.555 less than p less than 0.777 in the form Modifying above p with caret plus or minus Upper E.
Answer:
The modified representation is ![\r p \pm E = 0.666 \pm 0.111](https://tex.z-dn.net/?f=%5Cr%20p%20%5Cpm%20%20E%20%20%3D%200.666%20%5Cpm%20%200.111)
Step-by-step explanation:
From the question we are told that
The confidence interval interval is ![0.555 < p < 0.777](https://tex.z-dn.net/?f=0.555%20%3C%20%20p%20%3C%20%200.777)
Now looking at the values that make up the up confidence interval we see that this is a symmetric confidence interval(This because the interval covers 95% of the area under the normal curve which mean that the probability of a value falling outside the interval is 0.05 which is divided into two , the first half on the left -tail and the second half on the right tail as shown on the figure in the first uploaded image(reference - Yale University ) ) which means
Now since the confidence interval is symmetric , we can obtain the sample proportion as follows
![\r p = \frac{0.555 + 0.777}{2}](https://tex.z-dn.net/?f=%5Cr%20p%20%20%3D%20%20%5Cfrac%7B0.555%20%2B%200.777%7D%7B2%7D)
![\r p =0.666](https://tex.z-dn.net/?f=%5Cr%20p%20%20%3D0.666)
Generally the margin of error is mathematically represented as
![E = \frac{1}{2} * K](https://tex.z-dn.net/?f=E%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%2A%20%20K)
Where K is the length of the confidence interval which iis mathematically represented as
![K = 0.777 -0.555](https://tex.z-dn.net/?f=K%20%20%3D%20%200.777%20-0.555)
![K = 0.222](https://tex.z-dn.net/?f=K%20%20%3D%200.222)
Hence
![ME = \frac{1}{2} * 0.222](https://tex.z-dn.net/?f=ME%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%2A%20%200.222)
![ME = 0.111](https://tex.z-dn.net/?f=ME%20%20%3D%20%200.111)
So the confidence interval can now be represented as
![\r p \pm E = 0.666 \pm 0.111](https://tex.z-dn.net/?f=%5Cr%20p%20%5Cpm%20%20E%20%20%3D%200.666%20%5Cpm%20%200.111)
Answer:
A
Step-by-step explanation: