Answer: 0.0241
Step-by-step explanation:
The formula we use to find the margin of error :
![E=z^*\sqrt{\dfrac{p(1-p)}{n}}](https://tex.z-dn.net/?f=E%3Dz%5E%2A%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D)
, where z* = Critical value , n= Sample size and p = Sample proportion.
As per given , we have
n= 2400
Sample proportion of subjects showed improvement from the treatment:
![p=\dfrac{720}{2400}=0.3](https://tex.z-dn.net/?f=p%3D%5Cdfrac%7B720%7D%7B2400%7D%3D0.3)
Critical value for 99% confidence = z*= 2.576 (By z-table)
Now , the margin of error for the 99% confidence interval used to estimate the population proportion. :
![E=(2.576)\sqrt{\dfrac{0.3(1-0.3)}{2400}}](https://tex.z-dn.net/?f=E%3D%282.576%29%5Csqrt%7B%5Cdfrac%7B0.3%281-0.3%29%7D%7B2400%7D%7D)
![E=(2.576)\sqrt{0.0000875}](https://tex.z-dn.net/?f=E%3D%282.576%29%5Csqrt%7B0.0000875%7D)
![E=(2.576)(0.00935414346693)](https://tex.z-dn.net/?f=E%3D%282.576%29%280.00935414346693%29)
[Round to the four decimal places]
Hence, the margin of error for the 99% confidence interval used to estimate the population proportion. =0.0241
Answer: B
Triangle with the angle of 138 degrees
Step-by-step explanation:
I just did it on edg
Answer:
The decimal form of
.
Step-by-step explanation:
We proceed to find the decimal form of
, whose description is found below:
1) Multiplying the numerator by 100 and dividing it by 15:
Partial result: 0.06, Remainder: 10
2) Multiplying the remainder by the 10 and dividing it by 15:
Partial result: 0.066, Remainder: 10
3) Multiplying the remainder by the 10 and dividing it by 15:
Partial result: 0.0666, Remainder: 10
Since the decimal number is a infinite and periodical, we conclude that decimal form of
.
Answer:
(a) The manufacturer's claim is NOT overstated.
(b) The assumption of a normal population might be doubtful because the hourly distribution might vary during the day.
Step-by-step explanation:
(a) Let's use one-tailed Hypothesis Testing with:
: the population average is 530
α = 0.05
sample number n = 16
population average
= 530
sample average μ = 510
sample standard deviation σ = 50
If z < 1.645 then the hypothesis
is valid.
Let's calculate z =
= ![\frac{530-510}{50(4} = 8/5 = 1.6](https://tex.z-dn.net/?f=%5Cfrac%7B530-510%7D%7B50%284%7D%20%3D%208%2F5%20%3D%201.6)
Given that 1.6 < 1.645 then the hypothesis is valid.
Thus the manufacturer's claim is NOT overstated
(b) The hourly distribution might vary along the day. This is why the population might be not necessarily normal.