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
Lapatulllka [165]
3 years ago
8

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the e

ighth grade level. In an earlier study, the population proportion was estimated to be 0.21. How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 90% confidence level with an error of at most 0.03
Mathematics
1 answer:
Korolek [52]3 years ago
8 0

Answer:

A sample of 499 is needed.

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 zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is given by:

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

In this question, we have that:

\pi = 0.21

90% confidence level

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

How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 90% confidence level with an error of at most 0.03

We need a sample of n, which is found when M = 0.03. So

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

0.03 = 1.645\sqrt{\frac{0.21*0.79}{n}}

0.03\sqrt{n} = 1.645\sqrt{0.21*0.79}

\sqrt{n} = \frac{1.645\sqrt{0.21*0.79}}{0.03}

(\sqrt{n})^2 = (\frac{1.645\sqrt{0.21*0.79}}{0.03})^2

n = 498.81

Rounding up

A sample of 499 is needed.

You might be interested in
What is the lowest common denomimator of 14 and 26
Ludmilka [50]
Your answer is 182 :))
5 0
3 years ago
Read 2 more answers
How do I do orders of operations
shusha [124]

Step-by-step explanation:


Go from left to right doing any "A" or "S" as you find them. You can remember by saying "Please Excuse My Dear Aunt Sally".


(Brackets,Exponents,Divide,Multiply,Add,Subtract).

8 0
3 years ago
Read 2 more answers
Could someone explain how to solve this
ozzi

Answer:

y=\frac{4x}{5}-5

Step-by-step explanation:

linear equation

y=mx+b

We can see that when x=0 y= -5

THis means that b= -5 so we have

y=mx-5

We then know that when x=5 y= -1 so we have

-1=5m-5

Solve this and get m= 4/5

So we have

y=\frac{4x}{5}-5

7 0
2 years ago
Read 2 more answers
Nora uses 2 feet of ribbon to make a bow. She has 8 yards of ribbon. how many bows can she makes?
zimovet [89]
<span>She can make 12 bows because there are 3 feet in one yard so 8*3 is 24. then you divide 24 by 2 and you get 12 
</span>2ft ribbon=1bow
8 yards of ribbon
<span>1yard=3ft</span><span>
<u>She can make 12 bows!~</u>
<em>I hope this helps!~</em></span>
7 0
3 years ago
What is 31/10 as a mixed fraction
erma4kov [3.2K]
3 and 1 over 10 becasue 10 goes into 30 3 times
8 0
3 years ago
Other questions:
  • Alvin is inviting 7 friends to a party. If each friend will get 4 cookies and each box has 12 cookies, how many boxes does Alvin
    11·1 answer
  • Idk how people understand algebra help me
    9·1 answer
  • Lisa was finding the median of the heights of the people in her family: 54 inches, 48 inches, 68 inches, 67 inches, 73 inches. S
    7·1 answer
  • If Jesse wants to buy a $75,000 10-year term life insurance policy, and the annual premium rate (per $1000 of face value) for hi
    5·1 answer
  • Please answer #6-10
    11·1 answer
  • Katherine has $140 in the bank and is saving $6 per week. Abbie has $462 in the bank, but is spending at a rate of $10 per week.
    7·2 answers
  • A manufacturer of colored candies states that 13​% of the candies in a bag should be​ brown, 14​% ​yellow, 13​% red, 24​% ​blue,
    11·1 answer
  • A tortoise and hare are competing in a race. The function f and g are such that f(t) represents the tortoise's distance from the
    8·1 answer
  • Un objeto tiene una masa de 120 kg y un volumen de 5 m3. Calcula su densidad y determinada peso específico
    5·1 answer
  • Help with this i dont understand
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!