Question

Consider a simulation model to study the average daily cycle time for a product. Suppose you run the simulation model for 30 replications (days) and you obtain the sample average as 6.8 hours, with a sample standard deviation of 1.5 hours.

1) Calculate a 99% confidence interval for the long-run expected daily average cycle time.

2) On a particular day, predict the average cycle time for the parts produced on that day with a 99% confidence.

3) Which interval is wider? Is this always true? Why?

Answer 1

1)

sample mean 'x̄=	6.800
sample size   n=	30.00
sample std deviation s=	1.500
std error 'sx=s/√n=	0.274

for 99% CI; and 29 df, value of t=		2.7560
margin of error E=t*std error    =		0.755
lower bound=sample mean-E =		6.045
Upper bound=sample mean+E =		7.555
from above 99% confidence interval for population mean =(6.05,7.55)

2)

std errror of mean ='sx=s*√(1+1/n)=		1.525
for 99% CI; and 29 df, value of t=		2.756
margin of error E=t*std error    =		4.20
lower bound=sample mean-E =		2.598
Upper bound=sample mean+E=		11.002
from above 99% prediction interval for population mean =(2.60,11.00)

3)

prediction interval is wider since variability in an individual value is higher than average value