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. 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

%media:2excel.png%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 = 0.025. (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
Standard Deviation

(a-3) Choose the right option for H₀:μ_d ≤ 0; H₁: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.

• Yes

• No

Answer 1

Surgeon	Old Way	New Way	Difference(D)
1	39	28	11
2	59	38	21
3	33	20	13
4	43	37	6
5	56	49	7
		Total	58

sample mean=Md=sum of values of D/total

=58/5

=11.6

Old Way	New Way	Difference(D)	Dbar	D-dbar	(D-Dbar)^2
39	28	11	11.6	-0.6	0.36
59	38	21	11.6	9.4	88.36
33	20	13	11.6	1.4	1.96
43	37	6	11.6	-5.6	31.36
56	49	7	11.6	-4.6	21.16
	Total	58			143.2

sample standard deviation=sqrt(143.2/5-1)

=5.9833

sample mean=11.6

sample standard devaition=5.9833

df=n-1=5-1=4

=T.INV(0.025,4)

=2.776445

Reject if tcalc < 2.776445105

(a-4) Calculate the value of tcalc. (Round your answer to 4 decimal places.)

tcalc =Md/Sd/qrt(n)

=11.6/5.9833/sqrt(5)

= 4.335131

Tcal=4.3351

(b-1) Is the decision close? (Round your answer to 4 decimal places.)

The decision is close

The p-value is  =T.DIST.RT(4.335131,4)

0.0062

P value==0.0062

p<0.025

Reject Ho

(b-2) The new way is better than the old.

Yes

since p<0.05

(b-3) The difference is significant.

YES

sicne p=0.0123,p<0.025