1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Pani-rosa [81]
3 years ago
9

f the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many

students would need to be sampled?
Mathematics
1 answer:
Oksanka [162]3 years ago
7 0

Answer:

n=1849

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".  

The population proportion have the following distribution

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

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.005. And the critical value would be given by:

z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58

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 =\pm 0.03 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)  

Assuming that the proportion is estimated \hat p =0.5. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.03}{2.58})^2}=1849  

And rounded up we have that n=1849

You might be interested in
Katie received a speeding ticket that incurred a $125 fine. After one month, she will also
11Alexandr11 [23.1K]

Answer:

Try A

Step-by-step explanation:

3 0
2 years ago
Multiply mixed numbers 3 1/2 X 2 1/3
cricket20 [7]

Answer:

8 1/6

Step-by-step explanation:

that is da answer bbbbb

6 0
2 years ago
Read 2 more answers
Help me please ASAP please please
Likurg_2 [28]
X > -2....................
5 0
2 years ago
The line y+2x=b is perpendicular to a line that passes through the origin. If the two lines intersect at one point (k+2,2k), wha
Grace [21]

Answer:

The line y+2x=b is perpendicular to a line that passes through the origin. If the two lines intersect at the point (k+2,2k)

Step-by-step explanation:

that should be right

6 0
2 years ago
Carole purchased 7/8 of a pound of chocolate chips to make cookies.On the way home from the store she got hungry and ate 1/4 of
Oksi-84 [34.3K]
7/8 (0.875) minus 1/4(0.25) = 0.625 (5/8)
5 0
3 years ago
Other questions:
  • Which terms accurately classify this triangle? Choose exactly two answers that are correct. A. scalene B. obtuse C. acute D. iso
    12·1 answer
  • 4·p·4·p using exponets
    11·2 answers
  • Suppose there is a 13.4 % probability that a randomly selected person aged 30 years or older is a jogger. In​ addition, there is
    15·1 answer
  • On an airplane there are three seats on the left side in each row and two seats on the right side there are 45 seats total on th
    13·1 answer
  • What are the zeros of the equation X2 - 12x + 11 equals 0
    7·2 answers
  • Simplify the expression
    7·2 answers
  • Please help asap, will mark Brainliest xoxo
    8·1 answer
  • Alyssa plans to borrow $3,180 at 6.5% for 3.5 years . Find the amount of simple interest she should expect to pay.
    5·1 answer
  • Which is equivalent to <br> 4(x + 5)<br><br><br> 4x + 9<br> 4x + 20<br> 4x + 5
    15·2 answers
  • What is the domain of the function on the graph
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!