Question

Ten bottles of a certain carbonated beverage were tested for shelf life. The shelf lives obtained were: 108, 124, 124, 106, 115, 138, 163, 159, 134, 139 days. The population standard deviation is 19.5 days.

(a) Construct an appropriate 95% confidence interval for the overall mean shelf life of this carbonated beverage. Write out the full procedure that we went over in class. Give your answer in 2 decimal places.

(b) If someone said that the population mean shelf life was about 125 days, based on your confidence interval, would it be a plausible claim or not? State PLAUSIBLE or NOT PLAUSIBLE and give a brief reason for your answer.

(This is all that was asked)

Answer 1

a)

sample mean 'x̄=	131.000
sample size    n=	10.00
std deviation σ=	19.500
std error ='σx=σ/√n=19.5/√10=	6.1664

for 95 % CI value of z=		1.960
margin of error E=z*std error =6.1664*1.96=	12.09
lower bound=sample mean-E=131-12.09 =	118.91
Upper bound=sample mean+E=131+12.09=	143.09

from above 95% confidence interval for population mean =(118.91,143.09)

b)

since 125 falls within the confidence interval it is a  PLAUSIBLE value