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 0.044 Write only an integer as your answer. 10 Your 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 0.0207 MacBook Air

Explanation / Answer

Q.9 Pr(Operations result in complication) = 0.08

Margin of error = 0.044

Margin of error = Critical Test Statistic * Standard error of proportion

Critical Test Statistic (for alpha =99%) = 2.575

Standard error of proportion = sqrt(pq/N) = sqrt(0.08 * 0.92/ N)

0.044 = 2.575 * sqrt (0.08 * 0.92/N)

sqrt [N/ (0.08* 0.92)] = 2.575/0.044

N = 252.0733

or 253

Q.10Margin of error = Crtical Test Sttistic * Standard error of proportion

Crtical Test Sttistic (for alpha =99%) = 2.575

Standard error of proportion = sqrt(pq/N)

we will take p = q= 0.5 for minimum sample size

Standard error of proportion = sqrt(pq/N)= sqrt (0.5 * 0.5/N)

Margin of error =0.020 = 2.575 * 0.5/ n

n = 2.575 * 0.5/0.02 = 64.375

n = 4144.14 or 4145

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