Question

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 379 people aged 65 and over, 83 of them had sleep apnea. What is the lower bound for the 90% confidence interval for the proportion of those aged 65 and over who have sleep apnea. Round to three decimal places (for example: 0.419). Write only a number as your answer. Answer:

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 83 / 379 = 0.219

1 - = 0.781

Z = 1.28

Margin of error = E = Z* (( * (1 - )) / n)

= 1.28 * (((0.219 * 0.781) / 379)

= 0.027

Lower bound = - E = 0.219 - 0.027 = 0.192