Question

1. Comcast claims that mean waiting time of customers is 3 minutes with a standard deviation of 1 minute for customer service. A survey completed by an outside firm found in a sample of 50 Comcast customers that the mean waiting time was 2.75 minutes. At the .05 significance level, can we conclude that the mean waiting time is less than 3 minutes?

Answer 1

null hypothesis:Ho μ		=	3
Alternate Hypothesis:Ha μ		<	3
for 0.05 level with left tail test , critical z=			-1.645	(from excel:normsinv(0.05)
Decision rule:reject Ho if test statistic z<-1.645

population mean μ=		3
sample mean 'x̄=		2.750
sample size    n=		50
std deviation σ=		1.000
std error ='σx=σ/√n=1/√50=		0.1414
z statistic= ='(x̄-μ)/σx=(2.75-3)/0.141=		-1.77

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that the mean waiting time is less than 3 minutes