Question

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.H₀: m ³ 0          H₁: m < 0

b.H₀: m £ 0           H₁: m > 0

c.H₀: m = 0          H₁: m ¹ 0

The appropriate decision rule is:

a.Reject H₀ if ½t½ > t_{a/2, n-1}

b.Reject H₀ if t > t_{a, n-1}

c.Reject H₀ if t < - t_{a, n-1}

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

Answer 1

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
H₀ : ?_D = 0
H_A : ?_D > 0
Hypothesis test results:

Difference	Mean	Std. Err.	DF	T-Stat	P-value
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.