Answer:
The 99% lower confidence bound for the true average weight loss is 3.98 pounds.
This means that we can be 99% sure that the mean weight loss for all obese adults on a low-carb diet is positive.
Step-by-step explanation:
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
![\alpha = \frac{1-0.99}{2} = 0.005](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B1-0.99%7D%7B2%7D%20%3D%200.005)
Now, we have to find z in the Ztable as such z has a pvalue of
.
So it is z with a pvalue of
, so ![z = 2.575](https://tex.z-dn.net/?f=z%20%3D%202.575)
Now, find the margin of error M as such
![M = z*\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%2A%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In which
is the standard deviation of the population and n is the size of the sample.
![M = 2.575*\frac{19}{\sqrt{66}} = 6.02](https://tex.z-dn.net/?f=M%20%3D%202.575%2A%5Cfrac%7B19%7D%7B%5Csqrt%7B66%7D%7D%20%3D%206.02)
The lower end of the interval is the sample mean subtracted by M. So it is 11 - 6.02 = 3.98 pounds
The 99% lower confidence bound for the true average weight loss is 3.98 pounds.
This means that we can be 99% sure that the mean weight loss for all obese adults on a low-carb diet is positive.
Answer:
The critical value that should be used is T = 2.492.
The 98% confidence interval for the population mean bromide concentration is between 0.486 cc/m³ and 0.518 cc/m³
Step-by-step explanation:
We have the standard deviation for the mean, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 25 - 1 = 24
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of
. So we have T = 2.492, which is the critical value that should be used.
The margin of error is:
![M = T\frac{s}{\sqrt{n}} = 2.492\frac{0.0313}{\sqrt{25}} = 0.016](https://tex.z-dn.net/?f=M%20%3D%20T%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%20%3D%202.492%5Cfrac%7B0.0313%7D%7B%5Csqrt%7B25%7D%7D%20%3D%200.016)
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 0.502 - 0.016 = 0.486 cc/m³
The upper end of the interval is the sample mean added to M. So it is 0.502 + 0.016 = 0.518 cc/m³
The 98% confidence interval for the population mean bromide concentration is between 0.486 cc/m³ and 0.518 cc/m³
2: Reflecive Property
3: ASA
4: ASA
The answer is 113.4 because u divide 189 by 5 and the multiply the answer by 3 and u get your answer