______________ conveys information about the relative scarcity of a good, such as whether a shortage or a surplus exists.

An archaeologist uses an accelerator mass spectrometer to find the age of a buried branch. At the 68\%68%68, percent confidence

Komok [63]

Answer:

B. 10000 years old, with a margin of error of 400 years

Step-by-step explanation:

Assuming this complete problem: "12. An archaeologist uses an accelerator mass spectrometer to find the age of a buried branch. At the 68% confidence level, the spectrometer estimates that the branch was 10,000 years old with a following could the spectrometer estimate as the age of the branch at the 95% confidence level?"

The possible options are:

A. 9500 years old, with a margin of error of 500 years

B. 10000 years old, with a margin of error of 400 years

C. 9500 years olds, with a margin of error of 50 years

D. 10000 years old, with a margin of error of 40 year

Solution to the problem

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The margin of error for this case is given by this formula:

$ME= z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

For the first case the confidence was 68% so then $\alpha =1-0.68 =0.32$ and $\alpha/2 =0.16$ we can find a critical value on the normal standard distribution that accumulates 0.16 of the area on each tail and this value is $z=\pm 0.994$ , because P(z<-0.944) = 0.16 and P(Z>.944) = 0.16

The margin of error can be expressed like this:

$ME = z_{\alpha/2} SE$

We can solve for the standard error on this case and we got:

$SE = \frac{ME}{z_{\alpha/2}} =\frac{200}{0.994}=201.207$

And then for the new confidence interval we need to calculate the new $z_{\alpha}$ . For the first case the confidence was 95% so then $\alpha =1-0.95 =0.05$ and $\alpha/2 =0.025$ we can find a critical value on the normal standard distribution that accumulates 0.025 of the area on each tail and this value is $z=\pm 1.96$ , because P(z<-1.96) = 0.025 and P(Z>1.96) = 0.025. So then the new margin of error would be:

$ME = z_{\alpha/2} SE = 1.96*201.207=394.366$

The estimation for the mean not changes and from the before and new case is 1000 years. So then the best option for this case would be:

B. 10000 years old, with a margin of error of 400 years

And makes sense since a larger confidence interval means a wider interval.

8 0

3 years ago

Can you help me solve an infinite geometric sequence

zaharov [31]

A geometric series like

$\displaystyle \sum_{n=1}^\infty \dfrac{1}{\alpha^n}$

Converges if and only if $|\alpha|>1$ . If this is the case, the sum equals

$\displaystyle \sum_{n=1}^\infty \dfrac{1}{\alpha^n} = \dfrac{1}{\alpha-1}$

So, in your case, you have convergence if and only if

$|2+a|>1 \iff 2+a>1 \lor 2+a-1 \lor a$

And if this is the case, the sum equals

$\displaystyle \sum_{n=1}^\infty \dfrac{1}{(2+a)^n} = \dfrac{1}{2+a-1} = \dfrac{1}{a+1}$

8 0

3 years ago

We are interested in the dimensions of a certain square a rectangle had length triple the side of this square and width two unit

Sphinxa [80]

Let s be the side length of the square. The dimensions of the rectangle are three times the side of the square (i.e. 3s), and two less than the side of the square (i.e. s-2).

So, the area of this rectangle is

$3s(s-2)=3s^2-6s$

The area of the square is $s^2$ , and we know that the two areas are the same, so we have

$3s^2-6s=s^2 \iff 2s^2-6s=0 \iff 2s(s-3)=0 \iff s=0 \lor s=3$

The solution s=0 would lead to the extreme case where the rectangle and the square are actually a point, so we accept the solution s=3.

3 0

3 years ago

Halp, its math..

motikmotik

The answer is possibly 5x=5. Or x=1.

6 0

3 years ago

Read 2 more answers

One serving of whole milk contains 8 grams of fat. Reduced-fat milk contains 41.25% less fat per serving than whole milk. How ma

KiRa [710]

We are told the reduced fat milk has 41.25% less fat than whole milk.

So the reduced fat milk has 58.75% of the fat of whole milk (that is, 100% -41.25%).
A serving of whole milk has 8 grams of fat.
So a serving of reduced fat milk has .5875 * 8 g = 4.7 g of fat.

6 0

3 years ago