Question

A drapery store manager was interested in determining whether a new employee can install vertical blinds faster than an employee who has been with the company for two years. The manager takes independent samples of 10 vertical blind installations of each of the two employees and computes the following information.

	New Employee	Veteran Employee
Sample Size	10	10
Sample Mean	22.2 min	24.8 min
Standard Deviation	0.90 min	0.75 min

a) State the appropriate null and alternative hypotheses to test whether the new employee installs vertical blinds faster, on the average, than the veteran employee.

b) Calculate the pooled estimate of the common variance

c) Calculate the value of the test statistic

d) Set up the appropriate rejection region for the hypotheses in question i) assuming a = 0.05.

e) What is the appropriate conclusion?

Answer 1

a)

let new and veteren employees are populaiton 1 and 2,

null hypothesis:		μ1-μ2		=	0
Alternate Hypothesis:		μ1-μ2		<	0

b)

	new employee		veteran employee
x1                     =	22.2000	x2                     =	24.8000
s1                     =	0.9000	s2                    =	0.7500
n1                    =	10.0000	n2                    =	10.0000
pool. var S2p=	((n1-1)s21+(n2-1)*s22)/(n1+n2-2)=		0.6863

c)

Point estimate :		x1-x2                                     =	-2.6000
std error of difference=Se=		Sp*√(1/n1+1/n2)		=	0.3705
test stat t =		(x1-x2-Δo)/Se		=	-7.02

d)

for 0.05 level with right tailed test and n-1= 18 degree of freedom, critical value of t=					1.734
Decision rule :                   reject Ho if test statistic t<-1.734

e)

as test statitic is less than crtiical value we reject null hypothesis

we have sufficient evidence to conclude that new employee installs vertical blinds faster,on the average, than the veteran employee.