n article in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 273-279), considered arthroscopic meniscal repair with an absorbable screw. Results showed that for tears greater than 25 millimeters, 15 of 19 repairs were successful while for shorter tears, 21 of 29 repairs were successful. (a) Is there evidence that the success rate is greater for longer tears? Use . What is the -value? (b) Calculate a one-sided 95% confidence bound on the difference in proportions that can be used to answer the question in part (a). (a) There evidence that the success rate is greater for longer tears. The -value is Round your answer to four decimal places (e.g. 98.7654). (b) The one-sided 95% confidence bound is . Round your answer to three decimal places (e.g. 98.765).

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MrSmoot MrSmoot · Answer 1 · 2019-04-12T00:34:46+02:00

Answer:

a: There is not enough evidence to suggest that the success rate is greater for longer tears

b: 0.005 < p1 - p2 < 0.263

Step-by-step explanation:

We need to run a hypothesis test and also construct a confidence interval for a difference in two proportions.

p1 = 15/19

p2 = 21/29

The hypothesis for this test are:

H0: p1 - p2 = 0

HA: p1 - p2 > 0

*The alternate hypothesis states that the proportions of successes for longer tears is greater that the proportion of successes for shorter tears.

This is a 1 right tailed test

At 95% significance value, the critical z-score is z > 1.645

See attached photo 1 for the hypothesis test, and see attached photo 2 for the construction of the confidence interval.