How effective is gastric bypass surgery in maintaining weight loss in extremely

Question

How effective is gastric bypass surgery in maintaining weight loss in extremely obese people? A study conducted found that 76% of an SRS of 436 subjects who had received gastric bypass surgery maintained at least a 20% weight loss six years after surgery. (a) Are the conditions for the use of the large sample confidence interval met? Yes, there are at least 15 successes and 15 failures. Yes, there are exactly 15 successes and 15 failures. Yes, there is a combined total of at least 15 successes and failures. No, there are less than 15 successes and 15 failures. No, there are more than 15 successes and 15 failures. (b) Give a 90% confidence interval for the proportion of those receiving gastric bypass surgery that maintained at least a 20% weight loss six years after surgery. (Round your answers to four decimal places.) (c) Interpret your interval in the context of the problem. (Round your answers to two decimal places.) Based on this study, we estimate with 90% confidence that between % and % of all gastric bypass patients will maintain at least a 20% weight loss for six years after surgery. You may need to use the appropriate Appendix Table to answer this question.

Explanation / Answer

a) Yes there are at least 15 success and 15 failures

b)

here p=0.76

n=436

therefore std error =(p(1-p)/n)1/2 =0.0205

for 90% CI; z=1.645

therefore 90% confidence interval =point estimate -/+ z*std error =0.7264 ; 0.7936

c)

72.64% and 79.36%

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