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T-test or Z-test

You want to determine if your widgets from machine 1 are the same as machine 2. Machine 1 has a sample mean of 2000.21 and a sample standard deviation of 6.1 and a sample size of 2. Machine 2 has a sample mean of 1998.76 and a sample standard deviation of 6.2 with a sample size of 2. With an alpha of .05 can we claim that there is a difference between the output of the two machines? Which of the following statements are true?

a) We will reject the null hypothesis and prove there is a difference between the 2 populations.
b) We will not reject the null hypothesis and thus we can't prove there is a difference between the 2 populations.
c) Your alternative hypothesis could be stated as the population mean is less than 100.
d) Your null hypothesis could be stated as the population mean is greater than or equal to 100.
e) None of the above.

I selected "e" (none of the above) as the answer. Is that correct? I get confused as to when I should use the z-test and when I should use the t-test. Is the z-test for a population standard deviation and the t-test is for the sample standard deviation? So if I had to actually solve this problem, would I use the t-test? How would this look if it were solved? Please show all work!
Thanks!

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You want to determine if your widgets from machine 1 are the same as machine 2. Machine 1 has a sample mean of 2000.21 and a sample standard deviation of 6.1 and a sample size of 2. Machine 2 has a sample mean of 1998.76 and a sample standard deviation of 6.2 with a sample size of 2. With an alpha of .05 can we claim that there is a difference between the output of the two machines? Which of the following statements are true?

a) We ...

Solution Summary

The solution uses t-tests and z-tests to reject or except the null hypothesis in different scenarios.

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