Mathematics, 10.03.2020 05:29 JAYDENJONES0111

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.

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Answer from: heyrosaphoto3159

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).

Answer from: themaster66644

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] .

Answer from: Quest

here you hope this .

step-by-step explanation:

hypotenuse = √(15² + 8²)

= √(225 +64)

= √(289) = 17

sin(x) = cos(y) = 8/17

they are identical so long as you are doing the sine of one angle and the cosine of the only other angle that isn't the right angle.

Hurry need your use the image below to answer the following question. find the value of sin x° and

Answer from: Quest

c is the correct answer

step-by-step explanation:

9. find the determinant of k. a. 671 b. 913 c. 1 d. 597

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Sleep apnea: Sleep apnea is a disorder in which there are pauses in breathing during sleep. People w...

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