Asked Feb 15, 2020

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



Expert Answer

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 µ1 be the population mean for old machine and µ2 be the population mean for new machine.


Null hypothesis:


H0: µ1= µ2.


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


Alternative hypothesis:


H1: µ12.


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:

Statistics homework question answer, step 3, image 1


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