5) An experimental surgical procedure intended to reduce time to complete the op

Question

5) An experimental surgical procedure intended to reduce time to complete the operation is being studied as an alternative to the old method. Both methods are considered safe. Five surgeons perform the operation on two patients – using the old way on one patient and the new way on the other patient.

a) State the Hypothesis to show the new way of performing the surgery is faster than the old way.

b) Choose a level of Use = 0.05 for this problem.

c) The time to complete the surgical procedures for each of the five surgeons appear in the Surgery worksheet of the HW2 data workbook on Moodle. Collect data and calculate necessary statistics to test the hypothesis.

d) Sketch the sampling distribution. Include the critical value and test statistic.

e) Draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem.

f) What is the p-value for the hypothesis test?

g) Use Excel to perform the hypothesis test.

Old Way New Way Surgeon 1 36 29 Surgeon 2 55 42 Surgeon 3 28 30 Surgeon 4 40 32 Surgeon 5 62 56

Explanation / Answer

a)

Hypothesis:

Ho : uold - unew > 0

Ha: uold - unew < 0

c)

test statistic = 37.8 - 44.2/sqrt(11.41^2 + 13.97^2/5)

= -0.7934

rejection region : z <=-1.96 and z > 1.96

since it doesnot falls under rejection region , accept null hypothesis

Old Way New Way Surgeon 1 36 29 Surgeon 2 55 42 Surgeon 3 28 30 Surgeon 4 40 32 Surgeon 5 62 56 mean 44.2 37.8 standard deviation 13.97 11.41

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