In: Statistics and Probability
An experimental surgical procedure is being studied as an
alternative to the old method. Both methods are considered safe.
Five surgeons perform the operation on two patients matched by age,
sex, and other relevant factors, with the results shown. The time
to complete the surgery (in minutes) is recorded.
Surgeon 1 | Surgeon 2 | Surgeon 3 | Surgeon 4 | Surgeon 5 | |
Old way | 39 | 59 | 33 | 43 | 56 |
New way | 28 | 38 | 20 | 37 | 49 |
(a-1) Calculate the difference between the new and
the old ways for the data given below. Use α = .025.
(Negative values should be indicated by a minus
sign.)
X1 | X2 | X1 - X2 | |
Surgeon | Old Way | New Way | Difference |
1 | 39 | 28 | |
2 | 59 | 38 | |
3 | 33 | 20 | |
4 | 43 | 37 | |
5 | 56 | 49 | |
(a-2) Calculate the mean and standard deviation
for the difference. (Round your mean answer to 1 decimal
place and standard deviation answer to 4 decimal
places.)
Mean is ___________
Standard Deviation is ____________
(a-3) Choose the right option for
H0: μd ≤ 0;
H1: μd> 0.
a. Reject if tcalc > 2.776445105
b. Reject if tcalc < 2.776445105
(a-4) Calculate the value of
tcalc. (Round your answer to 4 decimal
places.)
(b-1) Is the decision close? (Round your
answer to 4 decimal places.)
The decision is ___________
a. close
b. not close .
The p-value is ____________
(b-2) The new way is better than the old.
a. No
b. Yes
(b-3) The difference is significant.
a. No
b. Yes