Question

A cruise company would like to estimate the average beer consumption to plan its beer inventory levels on future​ seven-day cruises.​ (The ship certainly​ doesn't want to run out of beer in the middle of the​ ocean!) The average beer consumption over 20 randomly selected​ seven-day cruises was 81,654 bottles with a sample standard deviation of 4,537 bottles. Complete parts a and b below.

a. Construct a 95​% confidence interval to estimate the average beer consumption per cruise.

The 95​% confidence interval to estimate the average beer consumption per cruise is from a lower limit of _____ bottles to an upper limit of _____ bottles. (Round to the nearest whole numbers.)

b. What assumptions need to be made about this population?

To find what assumptions need to be made about this​ population, carefully review the requirements for calculating a confidence interval with the​ Student's t-distribution when the sample size is less than or equal to 30.

(Please work this solution through Excel showing each step with the Excel formula.)

Answer 1

Solution:

n=20

df=n-1=20-1=19

alpha=0.05

alpha/2=0.05/2=0.025

t critical=

=T.INV(0.025,19)

=2.09302

95% confidence interval for mean  average beer consumption

xbar-t*s/sqrt(n),xbar+t*s/sqrt(n)

81654 -2.09302*4537 /sqrt(20),81654 +2.09302*4537 /sqrt(20)

79530.62, 83777.38

95% lower limit mean=79531

95% upper limit mean=83777

The 95​% confidence interval to estimate the average beer consumption per cruise is from a lower limit of 79531 bottles to an upper limit of 83777 bottles.

Solution-b:

population should follow normal distribution or sample size is large (n>30)

sample should be incependent

sample selected from popualtion is simple random sample