Mathematics, 16.01.2020 22:31 Jroc23

Apublic relations officer of william paterson university wants to estimate the mean iq of the university students. if she wants to be 99% confident that her sample mean is off by no more than 3 points, how many students she has to test in order to come up with a valid estimation?

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Answer from: xojade

$n=(\frac{2.58(15)}{3})^2 =166.41 \approx 167$

So the answer for this case would be n=167 rounded up to the nearest integer

Step-by-step explanation:

Assuming this complete problem: "A public relations officer of William Paterson University wants to estimate the mean IQ of the university students. If she wants to be 99% confident that her sample mean is off by no more than 3 points, how many students she has to test in order to come up with a valid estimation?. A recent study shows that IQ of New Jersey students has standard deviation of 15 points"

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".

Solution to the problem

The margin of error is given by this formula:

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

And on this case we have that $ME =\pm 3$ 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 99% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.005;0;1)", and we got $z_{\alpha/2}=2.58$ , replacing into formula (b) we got:

$n=(\frac{2.58(15)}{3})^2 =166.41 \approx 167$

So the answer for this case would be n=167 rounded up to the nearest integer

Answer from: Quest

It will b. 975 because i’m guessin
Select the correct answer. (image is below) construction is under way at an airport. this map shows

Answer from: Quest

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

$m=y/x=1/3$

the equation of the dashed line is

$y=(1/3)x$

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

$y> (1/3)x$

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

$m=(4-0)/(0-4)=-1$

the equation of the solid line is

$y=-x+4$

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

$y\leq-x+4$

step 3

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

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Apublic relations officer of william paterson university wants to estimate the mean iq of the univer...