Question 9 (1.5 points) A medical researcher wants to construct a 99% confidence

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Question 9 (1.5 points) A medical researcher wants to construct a 99% confidence interval for the proportion of knee replacement surgeries that result in complications. An article in the Journal of Bone and Joint Surgery suggested that approximately 8% of such operations result in complications. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.086 Write only an integer as your answer. Your Answer Answer Save Question 10 (1.5 points) A researcher wants to construct a 99% confidence interval for the proportion of people who changed jobs in the past year. What sample size is needed so that the confidence interval will have a margin of error of 0.023? Write only an integer as your answer.

Explanation / Answer

Answer 9

we have p =8% or 8/100 = 0.08

margin of error (ME) = 0.086

z score for 99% confidence level using normal distribution table is 2.576

using the formula for sample size n

sample size(n) = p*(1-p)[z/ME]^2

putting values below to solve for the value of n

n = 0.08*(1-0.08)*[2.576/0.086]^2 = 0.08*0.92*897.21 = 66.04

Rounding to nearest integer, we get sample size = 66

so, 66 knee replacement surgeries resulted in complications

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