2) 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 427 people aged 65 or over, 104 had sleep apnea. (please label your answers a, b, c etc) a) Find a point estimate of population proportion of those aged 65 and over have sleep apne b) Construct a 99% confidence interval for proportion of those over 65 or over have sleep apnea. c) Medical researchers claim more than 9% of elderly people have sleep apnea. Does the confidence interval contract their claim?
a)
Point estimate = = 104 / 427 = 0.244
b)
99% confidence interval for p is
- Z * sqrt ( ( 1 - ) / n) < p < + Z * sqrt ( ( 1 - ) / n)
0.244 - 2.576 * sqrt( 0.244 * 0.756 / 427) < p < 0.244 + 2.576 * sqrt( 0.244 * 0.756 / 427)
0.190 < p < 0.298
99% CI is ( 0.190 , 0.298 )
c)
Since 9% not contained in confidence interval , we have sufficient evidence to support the claim that
more than 9% of elderly people have sleep apnea.
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