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A manufacturer fills soda bottles. Periodically they test to see if there is a difference in...

A manufacturer fills soda bottles. Periodically they test to see if there is a difference in the amount of soda put in cola and diet cola bottles. A random sample of 14 cola bottles contains an average of 502 mL of cola with a standard deviation of 4 mL. A random sample of 16 diet cola bottles contains an average of 499 mL of cola with a standard deviation of 5 mL. Test the claim that there is a difference in the fill levels of the two types of soda using a 0.01 level of significance. Assume that the population variances are different since different machines are used for the filling process.

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