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
The sum of the measures of two angles is 90° one angle has a measure of 32.8° the other angle is represented by X what is the me
amid [387]

Answer:

x = 57.2

Step-by-step explanation:

Equation:

32.8 + x = 90

x = 90 - 32.8

x = 57.2

8 0
2 years ago
If biology is 40% and chemistry is 24% and earth science is blank and so is physics. There are 4% more students signed up for an
san4es73 [151]

Given data:

The given biology percentage is B=40%.

The given chemistry percentage is C=24%.

The percenage of earth science as compare to physics is E=P+4%.

The expresion for the sum of all subjects is,

B+C+E+P=100%

40%+24%+E+P=100%

E+P=36%.............................(I)

Substitute given value in the above expression.

P+4%+P=36%

2P=32%

P=16%

The nummber of students assigned earth science is,

E=16%+4%

=20%

Thus, the percentage of the students assigned to the physics subject is 16%.

6 0
1 year ago
10 QUESTIONS FOR THE TOTAL OF 50 POINTS!! PLEASE ANSWER QUICKLY!!!!! I NEED HELP AND FAST!!! AND WILL MARK BRAINLIEST!!!
prohojiy [21]

Answer:

  1. B) 48
  2. D) 81
  3. A) 11
  4. B) -81
  5. -246
  6. C) 5
  7. A) 19 9/25
  8. D) 11
  9. A) 48
  10. D) m-c/-b =a

Step-by-step explanation:

comment if you want the explanation, but you said you wanted it fast and it would take me like 10 minutes to right it all out

8 0
3 years ago
Read 2 more answers
I need help on this Algebra question
Phantasy [73]

Answer:

It is the third number Line

6 0
2 years ago
......................................
pantera1 [17]
your answer is 41.38
4 0
3 years ago
Other questions:
  • How to find the formula for distance between 2 skewed lines?
    6·1 answer
  • Is a negative and a positive equal a negative or positive in mutiplication
    10·1 answer
  • Express the inequality using interval notation. 3<×≤5
    15·1 answer
  • What is the magnitude of the resultant of z-y?<br> x=9i-j-2k<br> y=-6i+2j-k<br> z=-i+5j+3k
    13·2 answers
  • Need the answers for both #1 and #2 plz
    10·1 answer
  • Use the pattern of the rate of change to complete the table below that represents a
    8·1 answer
  • A student decided to research primate psychology for their science project. They measured how long it took gorillas to adapt to
    5·1 answer
  • How does the position of the decimal changes in a quotient as you divied by 10 100 1000
    8·1 answer
  • Can someone help me pls
    7·1 answer
  • What is 23 x 33 - 21
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!