In our solar system, 6 of the 8 planets have moons. What percentage of the planets have moons?

(1 point) Suppose we want a 95% confidence interval for the average amount spent on books by freshmen in their first year at col

Ne4ueva [31]

Answer:

a) $n=(\frac{1.960(16)}{5})^2 =39.33 \approx 40$

So the answer for this case would be n=40 rounded up to the nearest integer

b) For this case if we see the formula for the margin of error

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

We can see that the margin of error is inversely proportional to the sample size so if we want a samller margin of error we need a LARGER sample

Answer: LARGER

Step-by-step explanation:

Previous concepts

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

$\sigma=16$ represent the population standard deviation

n represent the sample size

Solution to the problem

Part a

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got $z_{\alpha/2}=1.960$ , replacing into formula (b) we got:

$n=(\frac{1.960(16)}{5})^2 =39.33 \approx 40$

So the answer for this case would be n=40 rounded up to the nearest integer

Part b

For this case if we see the formula for the margin of error

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

We can see that the margin of error is inversely proportional to the sample size so if we want a samller margin of error we need a LARGER sample

Answer: LARGER

5 0

2 years ago

How does the length of the hypotenuse in a right triangle relate to the lengths of the legs?

STALIN [3.7K]

It holds the legs up. there is a right angle which is the little box in the 90 degree corner:) the hypotenuse is always the longest part on the triangle which you can not simplify:) so the right triangle has legs that you can simplify:)

6 0

2 years ago

100 points + first decent answer gets brainliest

Ivahew [28]

Answer:

See explanation

Step-by-step explanation:

Selected theme park admission prices has the lower standard deviation.

Specific home stereo system's distribution is more spread out since the ratio between the standard deviation and the mean is greater compared to that of selected theme park admission prices.

specific home stereo system: 3.99/59=0.0676.

selected theme park admission prices: 4/1499=0.002668

0.0676>0.002668

8 0

10 months ago

Read 2 more answers

What can tradition teach you about cultures

cestrela7 [59]

Answer:

Traditions represent a critical piece of our culture. They help form the structure and foundation of our families and our society.

5 0

2 years ago