Question

SCENARIO 8-12   

The Three Brothers Energy Drink Company bottles and distributes a popular drink for athletes and exercise enthusiasts. Because of its marketing successes the company has installed an additional filling machine and the managers are eager to use it in daily operations. The machine is set to fill bottles at 16 oz.  

However, we know there is inherent machine variability and quality control has determined through testing a mean of 16.92oz. and a standard deviation of 0.56oz. using a 64 bottle sample.


Refer to Scenario 8-12.
Find a 87.7% confidence interval for the mean volume of the filled bottle contents.

Answer 1

Since , the population standard deviation is unknown.

Therefore , use t-distribution.

df=degrees of freedom=n-1=64-1=63

Significance level=

Now , ; the Excel function is , =TINV(0.123,63)

Therefore , the 87.7% confidence interval for the mean volume of the filled bottle contents is ,