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
Helga [31]
3 years ago
12

Sleep apnea: Sleep apnea is a disorder in which there are pauses in breathing during sleep. People with this condition must w up

frequently to breathe. In a sample of 432 people aged 65 and over, 108 of them had sleep apnea.
Construct a 99.5% confidence interval for the proportion of those aged 65 and over who have sleep apnea. Round the answer to three decimal places.
Mathematics
2 answers:
bonufazy [111]3 years ago
5 0

Answer:The required interval is (0.196, 0.030).

Step-by-step explanation:

Since we have given that

n = 432

x = 108

So, \hat{p}=\dfrac{x}{n}=\dfrac{108}{432}=0.25

at 99% level of confidence, z = 2.576

So, Margin of error would be

z\times \sqrt{\dfrac{pq}{n}}\\\\=2.576\times \sqrt{\dfrac{0.25\times 0.75}{432}}\\\\=2.576\times 0.021\\\\=0.0536

So, margin of error = 0.0536

Now, confidence interval would be

\hat{p}\pm 0.0536\\\\=(0.25-0.0536,0.25+0.0536)\\\\=(0.1964,0.3036)\\\\\approx (0.196,0.030)

Hence, the required interval is (0.196, 0.030).

Anvisha [2.4K]3 years ago
3 0

Answer:

99.5% confidence interval = [0.191 , 0.309]

Step-by-step explanation:

We are given that in a sample of 432 people aged 65 and over, 108 of them had sleep apnea.

The pivotal quantity for 99.5% confidence interval for the proportion of those aged 65 and over who have sleep apnea is given by;

           P.Q. = \frac{\hat p - p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } ~ N(0,1)

where, \hat p = sample proportion = 108/432 = 0.25

            p = population proportion

            n = sample size = 432

So, 99.5% confidence interval for the population proportion, p is given by;

P(-2.813 < N(0,1) < 2.813) = 0.995 {At 0.5% level of significance z table gives

                                                          critical value of 2.813}

P(-2.813 < \frac{\hat p - p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < 2.813) = 0.995

P(-2.813 * {\sqrt{\frac{\hat p(1-\hat p)}{n} } < {\hat p - p} < 2.813 * {\sqrt{\frac{\hat p(1-\hat p)}{n} } ) = 0.995

P(\hat p - 2.813 * {\sqrt{\frac{\hat p(1-\hat p)}{n} } < p < \hat p + 2.813 * {\sqrt{\frac{\hat p(1-\hat p)}{n} } ) = 0.995

99.5% confidence interval for p = [\hat p - 2.813 * {\sqrt{\frac{\hat p(1-\hat p)}{n} } , \hat p + 2.813 * {\sqrt{\frac{\hat p(1-\hat p)}{n} } ]

                               = [0.25 - 2.813 * {\sqrt{\frac{0.25(1-0.25)}{432} } , 0.25 + 2.813 * {\sqrt{\frac{0.25(1-0.25)}{432} } ]

                               = [0.191 , 0.309]

Therefore, 99.5% confidence interval for the proportion of those aged 65 and over who have sleep apnea is [0.191 , 0.309] .

You might be interested in
Three consecutive integers whose sum is -147
suter [353]

Step-by-step explanation:

Let the first integer be x

2nd integer = x + 1

3rd integer = x + 2

x + x + 1 + x + 2 = -147

3x + 3 = -147

3x = -147 - 3

3x = -150

x = -150 ÷ 3

x = -50

The three consecutive integers are

-50, -49, -48

5 0
3 years ago
A ball has a radius of 8 cm. What is the volume of the ball? Use 3.14 for pie Round your answer to the nearest tenth of a cubic
AveGali [126]

The volume of the ball is 33.5 cubic centimeter.

<u>Step-by-step explanation:</u>

It is given that, a ball has a radius of 8 cm.

We know that, the ball is in shape of the sphere.

The question is asked to find the volume of the ball.

To find the volume of the ball, you need to use the formula for volume of the sphere.

Volume of the sphere = (4/3)πr³

where,

  • π has the default value of 3.14
  • r is the radius of the ball.

Volume of the ball = (4/3)× 3.14× 8

⇒ 33.49

⇒ 33.5 (rounded to the nearest tenth)

⇒ 33.5 cubic centimeter.

∴ The volume of the ball is 33.5 cubic centimeter.

6 0
3 years ago
The perimeter of the square below is 36 yards. What is the length of each side? <br> yards
Inessa05 [86]

Answer:

9 yards

Step-by-step explanation:

36 divided by 4 = 9

3 0
2 years ago
Read 2 more answers
a chocolate company selects 800 random packages to check their weight. It finds that 12 packages have an incorrect weight. How m
Lerok [7]

Answer:

1.5% of 4000 or 60

Step-by-step explanation:

5 0
2 years ago
What is the surface area of this?
olchik [2.2K]
Find the area of two sides (Length*Height)*2 sides.
Find the area of adjacent sides (Width*Height)*2 sides.
Find the area of ends (Length*Width)*2 ends.
Add the three areas together to find the surface area.
Example: The surface area of a rectangular prism 5 cm long, 3 cm. Hope this helps?!
6 0
3 years ago
Other questions:
  • 7n+5=96 so what is the answer
    12·2 answers
  • What is the area of this triangle?
    12·2 answers
  • Ben is buying a tiny house. He will borrow $23,000 at a rate of 3% per year for 4 years. If the interest is compounded annually,
    6·1 answer
  • First right gets Brainliest!!!
    9·1 answer
  • What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point
    10·2 answers
  • Which of the following is a trinomial?
    6·2 answers
  • The sum of three numbers is 9. The sum of the first two numbers is 6 more than twice the third number. The second number is the
    7·1 answer
  • Convert the following improper fraction into a mixed number : 52/7
    9·1 answer
  • Find y if the line through the points (-4,y) and (8,2) has a slope of -1/3
    15·1 answer
  • URGENT NEED HELP. What is the approximate length of AB?
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!