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 below. The time to complete the surgery (in minutes) is recorded. At the .01 significance level, is the new way better?
Surgeon 1 
Surgeon 2 
Surgeon 3 
Surgeon 4 
Surgeon 5 

Old way 
36 
55 
38 
40 
62 
New way 
29 
42 
30 
32 
56 
The variable of interest (x) in this problem is:
a.Surgeons
b.Surgical procedure
c.Time to complete surgery (in minutes)
d.New Way and Old Way
e.None of the above
The problem involves:
a.Comparing the proportions of two populations
b.Comparing the variances of two populations
c.Comparing the means of two dependent populations
d.Comparing the means of two independent populations
e.None of the above
If the difference in time to complete the surgery is computed as Old Way minus New Way, the appropriate pair of hypotheses is:
a.H_{0}: m ³ 0 H_{1}: m < 0
b.H_{0}: m £ 0 H_{1}: m > 0
c.H_{0}: m = 0 H_{1}: m ¹ 0
The appropriate decision rule is:
a.Reject H_{0} if ½t½ > t_{a}_{/2, n1}
b.Reject H_{0} if t > t_{a}_{, n1}
c.Reject H_{0} if t <  t_{a}_{, n1}
What is the computed statistic equal to? ___________
At 0.01 significance level, which of the following statements would be the most appropriate given the statistical result from the sample?
a.There is no difference in the average time to complete the surgery between the surgeons
b.There is a difference in the average time to complete the surgery between the surgeons
cThere is no difference in the average time to complete the surgery between the two surgical methods
d.There is a difference in the average time to complete the surgery between the two surgical methods – the new way is better
eThere is a difference in the average time to complete the surgery between the two surgical methods – the old way is better
The statistical software output for this problem is:
Paired T hypothesis test:
?_{D} = ?_{1}  ?_{2} : Mean of the
difference between Old Way and New Way
H_{0} : ?_{D} = 0
H_{A} : ?_{D} > 0
Hypothesis test results:
Difference  Mean  Std. Err.  DF  TStat  Pvalue 

Old Way  New Way  8.4  1.2083046  4  6.9518895  0.0011 
Hence,
Variable of Interest: Time to complete surgery (in minutes)
The problem involves: Comparing the means of two dependent populations
Hypotheses: Option B is correct.
Decision Rule: Option B is correct.
Computed test statistic = 6.95
Statistical result: Option D is correct.
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