Question

You are the director of a cardiac surgical unit and you are interested in the difference between surgical times for experienced surgeons versus newly-trained surgeons. You collect data on a random selection of surgical operating room time (in minutes) for triple bypass surgery for 12 experienced surgeons and 14 newly-trained surgeons. The patients for all 26 surgeries were similar across a range of clinical and demographic characteristics. Use these data to answer the questions below. Show all supporting calculations.

Surgical Operating Room Time (minutes) Experienced Surgeons	Surgical Operating Room (minutes) Newly-Trained Surgeons
344	279
341	357
278	351
391	322
267	282
176	249
234	280
164	228
212	258
214	315
271	267
399	311
	312
	341

1. Assuming the distributions of surgical times for both types of surgeons are normally-distributed with known standard deviations of 80 minutes for experienced surgeons and 40 minutes for newly-trained surgeons, conduct the appropriate statistical test to determine if the mean surgical times differ between the two types of surgeons. Assume α=0.05.  

2. Subsequently you learned that the surgical operating room times for the newly-trained surgeons were incorrectly recorded and that each of the values were 30 minutes too short. What, if any, difference does this make to the conclusion you reached in question a?

Answer 1

Population standard deviation is given hence we will conduct a Z test for comparing to mean

a)

Since the null hypothesis is not rejected we have evidence that the mean surgical times do not differ between the two types of surgeons.

b) Increasing the dataset by a constant will increase the mean by the constant but the standard deviation will remain the same

Hence the sample mean for the newly-trained surgeons is 296.57+30 = 326.57

The conclusion will change as the null hypothesis is rejected.