Question

Suppose the span of thin iPhones has a population that is normally distributed with a standard deviation of 10. I sample 96 thin iPhones from this population and obtain a mean span of 58.81 and a standard deviation of 10.756. Using an alpha value of α = 0.05, is this observed mean significantly less than an expected span of 59?

Answer 1

null hypothesis:Ho μ		=	59
Alternate Hypothesis:Ha μ		<	59
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=		59
sample mean 'x̄=		58.810
sample size    n=		96
std deviation σ=		10.00
std error ='σx=σ/√n=10/√96=		1.0206
z statistic= ='(x̄-μ)/σx=(58.81-59)/1.021=		-0.19
p value        =		0.4247	(from excel:1*normsdist(-0.19)

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that observed mean is significantly less than an expected span of 59