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 | 40 | 60 | 31 | 38 | 64 |
New way | 32 | 44 | 35 | 36 | 53 |
Click here for the Excel Data File
(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.)
X_{1} | X_{2} | X_{1} - X_{2} | |
Surgeon | Old Way | New Way | Difference |
1 | 40 | 32 | |
2 | 60 | 44 | |
3 | 31 | 35 | |
4 | 38 | 36 | |
5 | 64 | 53 | |
(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 | |
Standard Deviation | |
(a-3) Choose the right option for H_{0}:
μ_{d} ≤ 0; H_{1}:
μ_{d}> 0.
Reject if t_{calc} > 2.776445105
Reject if t_{calc} < 2.776445105
(a-4) Calculate the value of
t_{calc}. (Round your answer to 4 decimal
places.)
t_{calc
}
(b-1) Is the decision close? (Round your
answer to 4 decimal places.)
The decision is (Click to
select) close not close .
The p-value is .
(b-2) The new way is better than the old.
No
Yes
(b-3) The difference is significant.
No
Yes
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(a - 1)
X1 Old way | X2 New way | X1 - X2 |
40 | 32 | 8 |
60 | 44 | 16 |
31 | 35 | -4 |
38 | 36 | 2 |
64 | 53 | 1 |
(a - 2)
From the values of X1 - X2, the following statistics are calculated:
(i)
Mean = = 4.6
(ii)
Standard Deviation = sd = 7.6681
(a - 3)
Correct option:
H0: μd ≤ 0; H1: μd > 0.
=0.025
df = 5 - 1 = 4
By Technology, critical value of t = 2.776445105
So,
Decision Rule:
Reject if tcalc > 2.776445105
(a - 4)
Test Statistic is got as follows:
(b -1)
Correct option:
not close
By Technology,
The p value is 0.1254
(b - 2)
Correct option:
No
(b - 3)
Correct option:
No
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