wo machines are used for filling oil with a net volume of 16.0 ounces. The filling processes are normal. The engineering suspects that both machines fill to the same net volume, whether or not this volume is 16.0 ounces. An experiment is performed by taking a random sample from the output of each machine. (α = 0.05) M 1 M 2 16.03 16.02 16.04 15.97 16.05 15.96 16.05 16.01 16.02 15.99 16.01 16.03 15.96 16.04 15.98 16.02 16.02 16.01 15.99 16.00 1) What are the hypotheses which should be tested? 2) Do the machines fill the same net volume?
Two machines are used for filling oil with a net volume of 16.0 ounces. The filling processes are normal. The engineering suspects that both machines fill to the same net volume, whether or not this volume is 16.0 ounces. An experiment is performed by taking a random sample from the output of each machine. (α = 0.05)
M 1 M 2
16.03 16.02
16.04 15.97
16.05 15.96
16.05 16.01
16.02 15.99
16.01 16.03
15.96 16.04
15.98 16.02
16.02 16.01
15.99 16.00
1) What are the hypotheses which should be tested?
2) Do the machines fill the same net volume?
Part 1:
The hypothesis to be tested are,
This is a two-tailed test.
We reject the null hypothesis if t-value < t-critical value.
Part 2:
To check whether the machines fill the same net volume we perform the two sample t-test for means.
Thus, from the given data we compute the means and the standard deviations for the two samples using the Excel formulas as AVERAGE And STDEV.S for mean and standard deviation respectively.
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