Question

In a test of a new surgical procedure, the five most respected surgeons in FlatBroke Township were invited to Carver Hospital. Each surgeon was assigned two patients of the same age, gender, and overall health. One patient was operated upon in the old way, and the other in the new way. Both procedures are considered equally safe. The surgery times are shown below:

Surgeon
	Allen				Bob				Chloe				Daphne				Edgar
Old way		36				55				28				40				62
New way		31				45				28				35				57

The time (in minutes) to complete each procedure was carefully recorded. In a right-tailed test for a difference of means, the test statistic is

Multiple Choice

• 1.645

• 1.860

• 2.132

• 3.162

Carver Memorial Hospital’s surgeons have a new procedure that they think will decrease the time to perform an appendectomy. A sample of 8 appendectomies using the old method had a mean of 38 minutes with a variance of 36 minutes, while a sample of 10 appendectomies using the experimental method had a mean of 29 minutes with a variance of 16 minutes. For a right-tailed test of means (assume equal variances), the test statistic is

Multiple Choice

• 3.814

• 2.365

• 1.895

• 3.000

Answer 1

1)

S. No	Old	New	diff:(d)=x1-x2	d2
1	36	31	5	25.00
2	55	45	10	100.00
3	28	28	0	0.00
4	40	35	5	25.00
5	62	57	5	25.00
	total	=	Σd=25	Σd2=175
	mean dbar=	d̅     =	5.000
	degree of freedom =n-1                            =		4
	Std deviaiton SD=√(Σd2-(Σd)2/n)/(n-1) =		3.535534
	std error=Se=SD/√n=		1.581139
	test statistic            =	(d̅-μd)/Se         =	3.162

2)

	Old	New
sample mean x =	38.000	29.000
standard deviation s=	6.000	4.000
sample size n=	8	10
Pooled Variance Sp2=((n1-1)s21+(n2-1)*s22)/(n1+n2-2)=			24.7500

Point estimate : x1-x2=		9.0000
std. error se =Sp*√(1/n1+1/n2)=		2.3598
test stat t =(x1-x2-Δo)/Se=		3.814