n a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2472 subjects randomly selecte
d from an online group involved with ears. 1022 surveys were returned. Construct a 99% confidence interval for the proportion of returned surveys.
1 answer:
Answer:
0.3876<p<0.4389
Step-by-step explanation:
-Given
-We calculate the proportion of surveys returned:
![\hat p=\frac{1022}{2472}\\\\=0.4134](https://tex.z-dn.net/?f=%5Chat%20p%3D%5Cfrac%7B1022%7D%7B2472%7D%5C%5C%5C%5C%3D0.4134)
For a 99% confidence interval:
![z_{\alpha/2}=2.576](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3D2.576)
#The margin of error is calculated as;
![ME=z_{0.005}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=2.576\times \sqrt{\frac{0.4134(1-0.4134)}{2472}}\\\\=0.0255](https://tex.z-dn.net/?f=ME%3Dz_%7B0.005%7D%5Ctimes%20%5Csqrt%7B%5Cfrac%7B%5Chat%20p%281-%5Chat%20p%29%7D%7Bn%7D%7D%5C%5C%5C%5C%3D2.576%5Ctimes%20%5Csqrt%7B%5Cfrac%7B0.4134%281-0.4134%29%7D%7B2472%7D%7D%5C%5C%5C%5C%3D0.0255)
The confidence interval are then:
![CI=\hat p\pm ME\\\\=0.4134\pm 0.0255\\\\=[0.3876,0.4389]](https://tex.z-dn.net/?f=CI%3D%5Chat%20p%5Cpm%20ME%5C%5C%5C%5C%3D0.4134%5Cpm%200.0255%5C%5C%5C%5C%3D%5B0.3876%2C0.4389%5D)
Hence, the confidence interval is 0.3876<p<0.4389
You might be interested in
3 (5+x)
You tripled 5+x
~JZ
D. no solution
Because they never found each other, the point they cross on is the solution.
Answer:
Domain:
(
−
∞
,
∞
)
,
{
x
|
x
∈
R
}
Range:
(
−
∞
,
68
]
,
{
y
|
y
≤
68
I hope this helped
Answer:
slope:2
(0,2)
Step-by-step explanation:
Answer:
62
Step-by-step explanation:
68+50+62= 180
all triangles must add up to 180