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
OLEGan [10]
2 years ago
13

Are you getting enough sleep? Many kids aren’t getting enough sleep, and TV might be part of the problem. Among 2002 randomly se

lected 8- to 18-year-olds in the United States, 71% had a TV in their bedroom. What is the lower boundary of our confidence interval at the 99% level?
a. 6547
b. 6714
c. 6677
d. 6839
Mathematics
1 answer:
Naya [18.7K]2 years ago
4 0

Using the z-distribution, it is found that the lower bound of the 99% confidence interval is given by:

d. 68.39%.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

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

In which:

  • \pi is the sample proportion.
  • z is the critical value.
  • n is the sample size.

In this problem, we have a 99% confidence level, hence\alpha = 0.99, z is the value of Z that has a p-value of \frac{1+0.99}{2} = 0.995, so the critical value is z = 2.575.

The sample size and estimate are given by:

n = 2002, \pi = 0.71

Hence, the lower bound is given by:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.71 - 2.575\sqrt{\frac{0.71(0.29)}{2002}} = 0.6839

Hence the lower bound is of 68.39%, which means that option D is correct.

More can be learned about the z-distribution at brainly.com/question/25890103

#SPJ1

You might be interested in
Suppose that the division N/5 leaves a remainder of 4, and the division N/2 leaves a remainder of 1, what is the ones digit on N
Tju [1.3M]

Since <em>N</em>/2 leaves a remainder, <em>N</em> must be odd and ends with 1, 3, 5, 7, or 9.

<em>N</em>/5 also leaves a remainder, so <em>N</em> is not divisible by 5, so it does not end in 5.

The only correct choice is then 9, since

1 = 0•5 + 1 and 1 = 0•2 + 1

3 = 0•5 + 3 and 3 = 1•2 + 1

7 = 1•5 + 2 and 7 = 3•2 + 1

9 = 1•5 + <u>4</u> and 9 = 4•2 + <u>1</u>

<u />

Alternatively, the given information is equivalent to saying

N\equiv 4\pmod5\\\\N\equiv1\pmod2

Then you can use the Chinese remainder theorem to find <em>N</em>.

7 0
3 years ago
Given the following triangle, what is the measure of the missing side?
Karolina [17]
It's a half of an equilateral triangle because their angles measure 30° and 60° (an equilateral triangle has 3 angles of 60°)
So x=(2h/√3)/2=h√3=27√3≈15.6
8 0
3 years ago
What's cot(-180)<br><img src="https://tex.z-dn.net/?f=%20%5Ccot%28%20-%20180%29%20" id="TexFormula1" title=" \cot( - 180) " alt=
kakasveta [241]
The answer is ~ 0.746999
6 0
3 years ago
Find all real square roots of −81 .
Lilit [14]
There are no real roots for a negative number, so -81 has no real roots, if the number is 81 however, then the tow roots are 9
3 0
3 years ago
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
Other questions:
  • Find the measure of the arc or central angle indicated ​
    8·1 answer
  • A group of three friends order a combo meal which includes two slices of pizza and a drink eight drink is priced at $2.50 if the
    5·1 answer
  • Correct answer gets brainliest and full ratings.
    12·2 answers
  • Please help me with this problem <br>3.14 = 22/7 and r = 7/4
    14·1 answer
  • Consider the function represented by the equation y-6x-9 +0. Which answer shows the equation written in function notation
    12·1 answer
  • Work out 4 1/7 + 1 1/2
    7·2 answers
  • Solve the following equation or inequality for the unknown variable. Round answer to two decimal places if necessary.
    13·1 answer
  • Ok i hope this is the last one 26 yd.=_in.
    15·2 answers
  • Help algebra 1 !! help me with this question
    12·1 answer
  • Which phrase best describes the translation from the graph y = 2(x - 15)2 + 3 to the graph of y = 2(x - 11)2 + 3?
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!