Mathematics, 24.12.2019 20:31 rpegler4

An investigator wants to estimate caffeine consumption in high school students.
a)- how many students would be required to ensure that a 95% confidence interval estimate for the mean caffeine intake (measured in mg) is within 15 units of the true mean? assume that the standard deviation in caffeine intake is 68mg

b)-how many students would be required to estimate the proportion of students who consume coffee? suppose we want the estimate to be within 5% of the true proportion with 95% confidence. show work.

Answers: 2

Show answers

Answers

Answer from: brennarfa

a) $n=(\frac{1.960(68)}{15})^2 =78.94 \approx 79$

So the answer for this case would be n=79 rounded up to the nearest integer

b) $n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16$

And rounded up we have that n=385

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 (variable of interest)

$\sigma$ represent the population standard deviation

n represent the sample size

Part a

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 =15 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:

$n=(\frac{1.960(68)}{15})^2 =78.94 \approx 79$

So the answer for this case would be n=79 rounded up to the nearest integer

Part b

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a*)

And on this case we have that ME = 0.05 and we are interested in order to find the value of n, if we solve n from equation (a*) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b*)

Since we don't have any info provided we can assume $\hat p =0.5$ . And replacing into equation (b*) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16$

And rounded up we have that n=385

Answer from: Quest

Idont knowgfdhdhfhggg.

Answer from: Quest

3/20

step-by-step explanation:

well, there are 20 outcomes, and 3 of them you want. so, 3/20

Another question on Mathematics

Mathematics, 21.06.2019 13:00

Determine the quotient and remainder when (6a3)+11a2-4a-9) is divided by (3a-2) express your answer in the form q(a) + r(a)/d(a)

Answers: 1

Answer

Mathematics, 21.06.2019 22:20

The school track has eight lanes. each lane is 1.25 meters wide. the arc at each end of the track is 180. the distance of the home straight and the radii for the arcs in the 1st 4 lanes are given. s=85m r1=36.5m r2=37.75m r3=39m r4=40.25m part one: find the radii of lanes 5 through 8 of the track. show your work. part two: if max ran around lane one, how far did he run? show your work and explain your solution. part three: max wants to run a total of three laps around the track, choose two additional lanes (2-8) for him to run and find the distance around those two lanes. show your work and round to the hundredths. part 4: based on your lane choices in part three, what was the total distance max ran in the three laps around the track?

Answers: 2

Answer

Mathematics, 21.06.2019 23:30

What is the volume of a rectangular crate that has dimensions 9 inches by 9 inches by 1 feet? 1,458 in.3 121.5 in.3 1,012.5 in.3 36 in.3

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

The bottom of ignacio's desktop is 74.5cm from the floor. ignacios sits in his adjustable chair, and the tops of his legs are 49.3cm from the floor. each clockwise rotation of the knob on the chair raises ignacio's legs by 4.8cm. write an inequality to determine the number of clockwise rotations, r, ignacio could make with the knob without his legs touching the desk.

Answers: 3

Answer

You know the right answer?

An investigator wants to estimate caffeine consumption in high school students.
a)- how many...

Questions

Mathematics, 20.08.2020 20:01

Choose the correct ray whose endpoint is B. ...

Mathematics, 20.08.2020 20:01

Carter is going on a 16.5 mile hike through the Grand Canyon if he wants to spread out his hike evenly over the next 6 hours how many miles should he...

Mathematics, 20.08.2020 20:01

Can someone help me out ...