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
1.What is the ratio of v to v max expressed as a percentage when [s] = 30 km
Helga [31]

Answer:

(a)96.77%

(b)3.23%

Step-by-step explanation:

Starting with the Michaelis-Menten equation which is used to model biochemical reactions:

Dividing both sides by V_{\max }}

\dfrac{v}{V_{max}}=\dfrac{[S]}{K_M + [S]}

Where: V_{\max }} = maximum rate achieved by the system

K_{\mathrm {M} }}=The Michaelis constant

{\displaystyle {\ce {[S]}}}= Substrate concentration

(a) When [S]=30K_M

\dfrac{v}{V_{max}}=\dfrac{[S]}{K_M + [S]}\\\dfrac{v}{V_{max}}=\dfrac{30K_M}{K_M + 30K_M}\\\dfrac{v}{V_{max}}=\dfrac{30}{1 + 30}\\\dfrac{v}{V_{max}}=\dfrac{30}{31}\\$Expressed as a percentage\\\dfrac{v}{V_{max}}=\dfrac{30}{31}X100=96.77\%

(b)When K_M=30[S]

\dfrac{v}{V_{max}}=\dfrac{[S]}{K_M + [S]}\\\dfrac{v}{V_{max}}=\dfrac{[S]}{30[S] + [S]}\\\\=\dfrac{1[S]}{30[S] + 1[S]}\\=\dfrac{1}{30 + 1}\\\dfrac{v}{V_{max}}=\dfrac{1}{31}\\$Expressed as a percentage\\\dfrac{v}{V_{max}}=\dfrac{1}{31}X100=3.23\%

8 0
3 years ago
River C is 300 Miles Longer than River D. If the sum of their lengths is 5,570 miles, what is the length of each river?
d1i1m1o1n [39]
x-\ length\ of\ river\ D\\
x+300-\ length\ of\ river\ C\\\\
5570=x+x+300\\
5570=2x+300\ \ \ | subtract\ 300\\5270=2x\ \ \ | divide\ by\ 2\\x=2635\\\\
River\ C\ is\ 2935miles\ long\ and\ river\ D\ 2635\ miles\ long.
6 0
3 years ago
Please help will mark brainiest
guapka [62]

Answer:

I think it is B, AB or CD and AB || CD

Step-by-step explanation:

8 0
3 years ago
An artist is deciding between two different triangular shapes to use for a sculpture. The first triangle has a base of 20 feet a
Kipish [7]
4 i belive altho  i could be way wrong
4 0
3 years ago
Select the correct answer.<br> Which of these is not a key feature of the function
kkurt [141]

Answer:

what is the answer to this question?

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • A bakery sells a giant decorated cookie for birthdays. The area of the cookie is about 113 square inches. What is the circumfere
    6·1 answer
  • What is the value of x?
    14·1 answer
  • Can someone help me with this khan academy question?
    5·1 answer
  • I really really need help​
    9·2 answers
  • A city council is considering funding a proposal to create a new city park. The council members will fund the proposal if they c
    8·1 answer
  • What is the slope for (3,-14) (15,19)
    15·1 answer
  • Help please :)))))))))))))))))))
    9·1 answer
  • Ms. Trimmer paid $65 last year for her subscription to Drama Teachers Monthly. This year the fee is $78. What rate of increase i
    15·2 answers
  • Write 4 1/7 as an improper fraction?
    9·1 answer
  • Graph the following inequality. y ≤ 3x +5 Use the graphing tool to graph the inequality Click to enlarge graph​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!