You want to determine if your widgets from machine 1 are the same as machine 2. Machine 1 has a sample mean of 5 and a population standard deviation 2 and a sample size of 4. Machine 2 has a sample mean of 10 and a population standard deviation of 2 with a sample size of 64. With an alpha of .01 can we claim that there is a difference between the output of the two machines. Which of the following statements are true?

Question

You want to determine if your widgets from machine 1 are the same as machine 2. Machine 1 has a sample mean of 5 and a population standard deviation 2 and a sample size of 4. Machine 2 has a sample mean of 10 and a population standard deviation of 2 with a sample size of 64. With an alpha of .01 can we claim that there is a difference between the output of the two machines. Which of the following statements are true?

Answer 1

What following statements?

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√n

If only one SD is provided, you can use just that to determine SEdiff.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. That should help you make your decision.