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
kipiarov [429]
2 years ago
6

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than ex

amine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 1% with 90% reliability, how many students would need to be sampled
Mathematics
1 answer:
amm18122 years ago
3 0

Answer:

6546 students would need to be sampled.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

The dean randomly selects 200 students and finds that 118 of them are receiving financial aid.

This means that n = 200, \pi = \frac{118}{200} = 0.59

90% confidence level

So \alpha = 0.1, z is the value of Z that has a p-value of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

If the dean wanted to estimate the proportion of all students receiving financial aid to within 1% with 90% reliability, how many students would need to be sampled?

n students would need to be sampled, and n is found when M = 0.01. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.01 = 1.645\sqrt{\frac{0.59*0.41}{n}}

0.01\sqrt{n} = 1.645\sqrt{0.59*0.41}

\sqrt{n} = \frac{1.645\sqrt{0.59*0.41}}{0.01}

(\sqrt{n})^2 = (\frac{1.645\sqrt{0.59*0.41}}{0.01})^2

n = 6545.9

Rounding up:

6546 students would need to be sampled.

You might be interested in
if y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8? a. 1/9 b. 2/3 c. 54 d. 96
Lapatulllka [165]
The value of y when x is 8 is b. 2/3
8 0
3 years ago
Read 2 more answers
Solve for x. Show each step of the solution 4.5 ( 8 - x ) + 36 = 102 - 2.5 ( 3x + 24)​
PSYCHO15rus [73]

Answer:

X=-10

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
a jar contains 36 marbles. it has 20 red, 12 black, and 4 green marbles. two marbles are drawn; the first is not returned before
Igoryamba
P(red) first drawn:
20/36=5/9
P(red) second drawn:
19/35

95/315 or 19/63. As a result, the probability that both marbles are red is 19/63. Hope it help!
7 0
3 years ago
Solve for x. x2 + 7x + 10 = 0
algol13
The answer is negative 80 or like this -80
6 0
3 years ago
Which ratio is equivalent to 6 : 7? A. 12 : 13 B. 18 : 48 C. 36 : 49 D. 48 : 56
lara [203]
The answer is D. The answer is D because you just keep multiplying each number by the same number.

6 • 8 = 48
7 • 8 = 56
6 0
3 years ago
Other questions:
  • HELP PLS MANY POINTS Use the function f(x) to answer the questions: f(x) = 4x2 + 8x − 5 Part A: What are the x-intercepts of the
    9·1 answer
  • Identify all of the radii of circle O<br><br> PLEASE HELP!!
    7·1 answer
  • Simplify using exponent rules.<br><br> (3x^4) (-6x)<br><br><br> (SHOW YOUR WORK)
    13·1 answer
  • Triangle ABC with vertices A(4, −6), B(2, −8), and C(−10, 4) is dilated by a scale factor of 2 to obtain triangle A′B′C′. Which
    13·1 answer
  • Solve for x.<br> 5x– 2(x+1) =1/4<br><br> Enter your answer in the box.<br><br> X=_
    7·1 answer
  • Explain how to use a cordinate plane to find the area of a rectangle with vertices (-4,9) (-4-3) (-1,-3) and(-1,9) . What is the
    5·1 answer
  • Given AD = 7x , AB = 3x and the perimeter is 160. Find X.
    9·1 answer
  • there are 20 total students in Kim's class. 12 of the students are boys and 8 are girls. which of the following reqesents the pa
    7·1 answer
  • What are the domain and range of this function
    12·1 answer
  • Please help me solve
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!