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
Troyanec [42]
2 years ago
9

Reading proficiency: An educator wants to construct a 99.5% confidence interval for the proportion of elementary school children

in Colorado who are proficient in reading.
The results of a recent statewide test suggested that the proportion is 0.69.

Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.07?
Mathematics
1 answer:
Shkiper50 [21]2 years ago
4 0

Answer:

A sample size of 345 is needed so that the confidence interval will have a margin of error of 0.07

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 of the interval is given by:

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

In this problem, we have that:

p = 0.69

99.5% confidence level

So \alpha = 0.005, z is the value of Z that has a pvalue of 1 - \frac{0.005}{2} = 0.9975, so Z = 2.81.

Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.07?

This is n when M = 0.07. So

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

0.07 = 2.81\sqrt{\frac{0.69*0.31}{n}}

0.07\sqrt{n} = 1.2996

\sqrt{n} = \frac{1.2996}{0.07}

\sqrt{n} = 18.5658

(\sqrt{n})^{2} = (18.5658)^{2}

n = 345

A sample size of 345 is needed so that the confidence interval will have a margin of error of 0.07

You might be interested in
How can you rewrite P(z £ –1.75) in order to find the answer? P(z £ 1.75) P(z ³ -1.75) 1 - P(z £ -1.75) 1 - P(z £ 1.75)
Fudgin [204]
To rewrite it the answer is 1-P(z 1.75) D

5 0
3 years ago
Read 2 more answers
List all the factors of 16
Olenka [21]

Answer:

There are 5 factors of 16, which are 1, 2, 4, 8, and 16. 

5 0
2 years ago
Read 2 more answers
25 POINTS! Over what interval is the function nonlinear?
andreyandreev [35.5K]

Answer:

-2 < x  < 2

Step-by-step explanation:

6 0
2 years ago
What is the reason that m&lt;2 and m&lt;3 are supplementary
katen-ka-za [31]

Answer:

see explanation

Step-by-step explanation:

∠2 and ∠3 are same- side interior angles and are supplementary.

6 0
3 years ago
Ximena is typing a 2500 word essay. In 9 minutes she types 396 words, at this rate can Ximena type the essay in an hour?
sasho [114]

Answer:

yes

Step-by-step explanation:

396÷ 9= 44

44×60= 2,640 > 2500

8 0
2 years ago
Other questions:
  • Joe deposits $50,000.00 in an account that earns 8.3% simple interest. About how many years will it take for his account balance
    6·2 answers
  • Teresita worked part-time for 2 weeks in a pharmacy. During the second week, she worked 13 times the
    12·2 answers
  • What is the circumference of the circle shown below, given that the length of AC (the minor arc) is 8?
    7·2 answers
  • Ad
    10·1 answer
  • A quadratic function has its vertex at the point (- 3, 8) . The function passes through the point (0, 0) . When written in verte
    12·1 answer
  • If a circle has a radius of 5 meters, what<br> is the diameter?
    6·1 answer
  • In ΔQRS, the measure of ∠S=90°, RS = 2.2 feet, and QR = 4.5 feet. Find the measure of ∠Q to the nearest tenth of a degree.
    6·1 answer
  • Need help on the 2 questions ASAP and SHOW WORK PLEASE !!!! 50 points ????
    10·1 answer
  • Find g (-6) if g (x)=5 x - 7
    5·1 answer
  • How many triangles can be formed by joining the vertices of an octagon?need answer and solution pls​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!