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StatisticsQ&A Librarythe old machine filled 12 soda cans with an average of 11.9 oz of soda with a standard deviation of 0.3 ounces. the new machine still fills them (11 cans) with an average of 12.1 ounces, with a standard deviation of 0.3 oz. is the new machine filling with significantly more than the old machine? (a=.05) show all work pleaseQuestion

Asked Feb 15, 2020

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the old machine filled 12 soda cans with an average of 11.9 oz of soda with a standard deviation of 0.3 ounces. the new machine still fills them (11 cans) with an average of 12.1 ounces, with a standard deviation of 0.3 oz. is the new machine filling with significantly more than the old machine? (a=.05) show all work please

Step 1

From the given information, the claim of the problem is new machine is filling with significantly more than the old machine.

Let us define µ_{1} be the population mean for old machine and µ_{2} be the population mean for new machine.

** **

**Null hypothesis:**

* *

*H*_{0}: µ_{1}= µ_{2}.

That is, the average filling of soda is equal for old machine and new machine.

**Alternative hypothesis:**

* *

*H*_{1}: µ_{1}<µ_{2}.

** **

That is, the average filling of soda for new machine is significantly more than old machine.

Step 2

For old machine:

Sample mean: 11.9

Sample standard deviation: 0.3

Sample size: 12.

For new machine:

Sample mean: 12.1

Sample standard deviation: 0.3

Sample size: 11.

Step 3

The test statistic is **-1.5971** and it is calculated below:

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