A cruise company would like to estimate the average beer con

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 81,745 bottles with a sample standard deviation of 4,587 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 (blank) bottles to an upper limit of (blank) bottles.

(Round to the nearest whole numbers.)

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

A.

The only assumption needed is that the population size is larger than 30.

B.

The only assumption needed is that the population follows the Student\'s t-distribution.

C.

The only assumption needed is that the population distribution is skewed to one side.

D.

The only assumption needed is that the population follows the normal probability distribution.

Solution

a)

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    81745          
t(alpha/2) = critical t for the confidence interval =    2.093024054          
s = sample standard deviation =    4587          
n = sample size =    20          
df = n - 1 =    19          
Thus,              
              
Lower bound =    79598.21792          
Upper bound =    83891.78208          
              
Thus, the confidence interval is              
              
(   79598.21792   ,   83891.78208   ) [ANSWER]

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b)

D. The only assumption needed is that the population follows the normal probability distribution.