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# t-statistics with interpretation and assumptions

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Consider the filling operation for 20-oz bottles of a popular soft drink. Historically, this operation averages 20.2 oz. A recent random sample of 12 bottles yielded these volumes:
20.0 20.1 20.0 19.9 20.5 20.9
20.1 20.4 20.2 19.1 20.1 20.0
a. Find the sample mean for these data.
b. Assume that the historical average is true. Calculate the observed value of t-statistics. Use the rule of thumb to interpret your results.
c. What did you assume to do the informal analysis? Can you evaluate how well data meet the assumption? If yes, determine how comfortable you are with them. If not, explain why.

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#### Solution Preview

Step wise solution is provided for the attached problem so that it can be easy to understand.

Solution:
Part (a)
Sample Mean is given by
= ∑Xi/ n = 20.10833333 = 20.108 (app)
Part (b)
Here we have
µ = 20.2
n= 12
s = Sample Standard ...

#### Solution Summary

In this solution, you will get the calculation of t-statistics, sample mean, interpretation of t-statistics results and assumptions of t-test. Each and everything is explained well in the solution for better clarity.

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