In Knee surgery, Results showed that for tears longer than 25 millimeters, 14 out of 18 repairs were successful, meanwhile for shorter tears, 22 out of 30 repairs were successful in the surgery. (i) If no estimation of the sample proportion for the longer tears that were successful given, what sample size is needed if we are 90% confident that the margin of error can be reduced to 1%?  (ii) Calculate a 93% one-sided upper bound confidence interval on the difference in proportion between longer tears and shorter tears that were unsuccessful in the surgery.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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APPLIED STATISTICS

In Knee surgery, Results showed that for tears longer than 25 millimeters, 14 out of 18 repairs were successful, meanwhile for shorter tears, 22 out of 30 repairs were successful in the surgery.

(i) If no estimation of the sample proportion for the longer tears that were successful given, what sample size is needed if we are 90% confident that the margin of error can be reduced to 1%? 

(ii) Calculate a 93% one-sided upper bound confidence interval on the difference in proportion between longer tears and shorter tears that were unsuccessful in the surgery.

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