Question

A soft-drink machine at a restaurant is regulated so that amount of drink dispensed is normally distributed with an average of 200 millilitres and a standard deviation of 15 millilitres. The machine is checked periodically by taking sample drinks and computing the average content. Restaurant manager has recently received complaints from customers about underfilling drinks (less filled than usual). Test the customers claim at the 5% level of significance If the averaged volume for a sample of 9 randomly selected drinks is 196 millilitres.

Answer 1

null hypothesis:Ho μ		=	200
Alternate Hypothesis:Ha μ		<	200

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=		200
sample mean 'x̄=		196.000
sample size    n=		9
std deviation σ=		15.000
std error ='σx=σ/√n=15/√9=		5.0000
z statistic= ='(x̄-μ)/σx=(196-200)/5=		-0.80

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 the drinks are under filled.