Question

Question 4 (0.5 points) 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 339 people aged 65 and over, 112 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. Your Answer

Answer 1

Problem 4 Given Favorable for X 112 X sample size 339 n Sample proportion Sample proportion 0.3304 Critical z value level of confidence С 0.9 Level of significance 0.1 = Critical z 1.645 -1.6448536 p(1-p) 90 % Confidence interval is (1-p) =p -z Lower limit =0.3304-1.645*V(0.6604(1-0.3304)/339) п Lower bound is 0.2884

Question 5 Given Favorable for x 119 X sample size 486 Sample proportion Sample proportion 0.2449 Critical z value level of confidence С 0.99 Level of significance 0.01 Critical z -2.5758293 2.576 p (1-p) 99 % Confidence interval is п (1-p) -0.2449 +2.576*V(0.2449(1-0.2449)/486) Upper limit =p+z п 0.295

Question 6 Given Favorable for x 212 х = sample size 389 = Sample proportion Sample proportion 0.5450 Critical z value level of confidence С 0.95 = Level of significance 0.05 Critical z -1.959964 1.96 p(1-p) 95% Confidence interval is п (1-p) =p -z | =0.5450-1.96*V(0.5450(1-0.5450)/389) Lower limit п 0.496

Question 7 Given Favorable for x 157 X = sample size 506 n Sample proportion Sample proportion 0.3103 Critical z value level of confidence C 0.99 = Level of significance 0.01 = Critical z -2.5758293 2.576 P(1-p) 99 % Confidence interval is n (1-p) -0.3103+2.576*V(0.3103(1-0.3103)/506) Upper limit n 0.363

Answer 2

Q4 only done :

SOLUTION :

4.

Proportion of apnea , p = 112/339 = 0.3304 

SD = sqrt(p(1-p)) = sqrt(112/339 * (1 - 112/339)) = 0.4704 

SD of p = 0.4704/sqrt(n) = 0.4704)/sqrt(339) = 0.02555

For 90% confidence level, z = +/- 1.645 

So, lower limit of p at 90% Confidence Interval

= - z * SD + p 

= - 1.645 * 0.02555 + 0.3304

= 0.2884 

= 0.289 (ANSWER).