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# Hypothesis Testing Widgets

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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 500 and a population standard deviation of 6 and a sample size of 18. Machine 2 has a sample mean of 500.5 and a population standard deviation of 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. The critical values you will use are 1.96 and -1.96
d. B and C are correct
e. None of the above are correct

Do you use the t-test for this answer? Do the t-test and z-test give different answers?