Answer:
y
=
−
1
/2
x
+
2 is slope
Step-by-step explanation:
Hope this helps.
Answer:
The answer is "(0.73,0.87)".
Step-by-step explanation:
Given:
number of girls![= 64](https://tex.z-dn.net/?f=%3D%2064)
number of boys![= 16](https://tex.z-dn.net/?f=%3D%2016)
Total number of children![= 64+16= 80](https://tex.z-dn.net/?f=%3D%2064%2B16%3D%2080)
So,![n=80](https://tex.z-dn.net/?f=n%3D80)
Calculating the value of the proportion which is given by girls:
![\hat{p}= \frac{\text{number of girls}}{\text{total number of childrens}}](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%20%5Cfrac%7B%5Ctext%7Bnumber%20of%20girls%7D%7D%7B%5Ctext%7Btotal%20number%20of%20childrens%7D%7D)
![=\frac{64}{80}\\\\=\frac{8}{10}\\\\= 0.8](https://tex.z-dn.net/?f=%3D%5Cfrac%7B64%7D%7B80%7D%5C%5C%5C%5C%3D%5Cfrac%7B8%7D%7B10%7D%5C%5C%5C%5C%3D%200.8)
Therefore the confidence interval is:
![\to \hat{p}\pm z_{(1-\frac{\alpha }{2})}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\\to 0.8 \pm 1.75\sqrt{\frac{0.8(1-0.8)}{80}}\\\\\to 0.8 \pm 1.75 \sqrt{\frac{0.8(0.2)}{80}}\\\\\to 0.8 \pm 1.75 \sqrt{\frac{0.16}{80}}\\\\\to 0.8 \pm 1.75 \sqrt{0.002}\\\\\to 0.8 \pm 1.75 (0.04)\\\\\to 0.8 \pm 0.07\\\\\to (0.73,0.87)](https://tex.z-dn.net/?f=%5Cto%20%5Chat%7Bp%7D%5Cpm%20z_%7B%281-%5Cfrac%7B%5Calpha%20%7D%7B2%7D%29%7D%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%5C%5C%5C%5C%5Cto%200.8%20%5Cpm%201.75%5Csqrt%7B%5Cfrac%7B0.8%281-0.8%29%7D%7B80%7D%7D%5C%5C%5C%5C%5Cto%200.8%20%5Cpm%201.75%20%5Csqrt%7B%5Cfrac%7B0.8%280.2%29%7D%7B80%7D%7D%5C%5C%5C%5C%5Cto%200.8%20%5Cpm%201.75%20%5Csqrt%7B%5Cfrac%7B0.16%7D%7B80%7D%7D%5C%5C%5C%5C%5Cto%200.8%20%5Cpm%201.75%20%5Csqrt%7B0.002%7D%5C%5C%5C%5C%5Cto%200.8%20%5Cpm%201.75%20%280.04%29%5C%5C%5C%5C%5Cto%200.8%20%5Cpm%200.07%5C%5C%5C%5C%5Cto%20%280.73%2C0.87%29)
![\therefore \\\\\text{The lower confidence limit} = 0.73\\\\\text{The upper confidence limit} = 0.87\\](https://tex.z-dn.net/?f=%5Ctherefore%20%5C%5C%5C%5C%5Ctext%7BThe%20lower%20confidence%20limit%7D%20%3D%200.73%5C%5C%5C%5C%5Ctext%7BThe%20upper%20confidence%20limit%7D%20%3D%200.87%5C%5C)
Answer:
Two solutions.
Step-by-step explanation:
I have attached the work to your problem.
Please see the attachment below.
I hope this helps!