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# Population and Sample Standard Deviation

1.)If the population standard deviation ( s) is known then we use it in calculating the z-statistic as follows.
z= [Xbar - m ] / [ s/ sqrt(n) ]

On the other hand if population standard deviation is unknown, we substitute the sample standard deviation (s) in place of population standard deviation in calculating the z-statistic.
z= [Xbar - m ] / [ s/ sqrt(n) ]

Exercise:
A soda bottling machine is filling 32 oz. soda cans. We observe the machine filling 35 bottles (picked at random) and obtain the following data:

32.12 32.04 32.04 32 32.01 32.12 32.05
32.13 32.05 32.05 31.72 32.08 32.03 31.95
32.02 32.22 32.22 32.22 31.89 32.2 32.22
31.73 31.95 31.95 32.07 32.13 32.13 31.73
31.98 32.21 32.21 31.97 32.09 31.97 32.12

As a bottler we want to know if the machine was underfilling. Setup Null and Alternate hypotheses to test if average amount of soda in each can is less than 32 oz. Please test the hypothesis using a = 0.05. What can you conclude from all this?

#### Solution Summary

This solution provides a null and alternative hypothesis and calculates the test statistic to compare with the level of significance in order to accept or reject the null hypothesis.

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