Sleep apnea is a disorder in which there are pauses in breathing during sleep. People with this condition must wake up frequently to breathe. In a sample of 431 people aged 65 and over, 109 of them had sleep apnea. (a) Find a point estimate for the population proportion of those aged 65 and over who have sleep apnea. Round the answer to at least three decimal places. The point estimate for the proportion of those aged 65 and over who have sleep apnea is .253. (b) Construct a 98% confidence interval for the proportion of those aged 65 and over who have sleep apnea. Round the answer to at least three decimal places. A 98% confidence interval for the proportion of those aged 65 and over who have sleep apnea is
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The margin of error is given by the formula: \(ME = Z \times \sqrt{\frac{p(1-p)}{n}}\), where \(Z\) is the z-score corresponding to the confidence level, \(p\) is the sample proportion, and \(n\) is the sample size. Show more…
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Joanna Q.
Sleep apnea: Sleep apnea is a disorder in which there are pauses in breathing during sleep. People with this condition must wake up frequently to breathe. In a sample of 434 people aged 65 and over, 106 of them had sleep apnea. A) The point estimate for the proportion of those aged 65 and over who have sleep apnea is 0.244. B) Construct a 99.8% confidence interval for the proportion of those aged 65 and over who have sleep apnea. Round the answer to at least three decimal places. A 99.8% confidence interval for the proportion of those aged 65 and over who have sleep apnea is __< p <__. C) In another study, medical researchers concluded that more than 31% of elderly people have sleep apnea. Based on the confidence interval, does it appear that more than 31% of people aged 65 and over have sleep apnea? Explain. Since all of the values in the confidence interval are Greater Than/Lesser Than(Choose one) 0.31, then the confidence interval Does/Does Not(Choose one) contradict the claim.
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