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hypothesis test - bottling machine functioning properly

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Bubble Bottling Co. is operating an old machine that fills each one-liter plastic bottle of soda prior to capping. The average fill seems O.K., but the operator has reported lately that too many bottles seem either too full or too empty coming off the line. The problem, of course, could be the variation in the capacity of the bottles rather than with the machine's ability to fill them. The filling machine is rated at a standard deviation of 0.01 liter. In an effort to get to the bottom of the situation, you decide to open up 30 filled bottles and measure the volume of the contents. The sample variance is computed at 0.00012 liters.
a. State the appropriate null and alternative hypotheses.
b. Calculate the test statistic.
c. At  = 0.05, should you reject the null hypothesis?
d. What conclusion can you draw?

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Solution Summary

The following solution demonstrates the process of performing a hypothesis test to determine if a bottling machine is functioning properly.

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a. State the appropriate null and alternative hypotheses.

Ho: M=0.01, i.e. the mean capacity of the bottle is 0.01 liter
Ha: M<>0.01, i.e. the mean capacity of the bottle is NOT 0.01 liter

b. Calculate the test statistic.

I doubt if 0.00012 liter is the Variance or Standard deviation, because it's too ...

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