You want to determine if your widgets from machine 1 are the same as machine 2.

Question

You want to determine if your widgets from machine 1 are the same as machine 2. Machine 1 has a sample mean of 15.1 and a population standard deviation 5 and a sample size of 12.5. Machine 2 has a sample mean of 14.9 and a population standard deviation of 6 with a sample size of 12. 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?

A. We will not reject the null hypothesis B. The resulting test statistic will be less than 1 C. The critical values you will use are 1.96 and -1.96 D. A and B are correct E. A, B, and C are correct

Explanation / Answer

Let mu1 be the mean for Machine 1

Let mu2 be the mean for Machine 2

The test hypothesis:

Ho: mu1=mu2 (i.e. null hypothesis)

Ha: mu1 not equal to mu2 (i.e. alternative hypothesis)

The test statistic is

Z=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)

=(15.1-14.9)/sqrt(5^2/12+6^2/12)

=0.09

It is a two-tailed test.

Given a=0.01, the critical values are Z(0.005) = -2.58 or 2.58 (from standard normal table)

The rejection regions are if Z<-2.58 or Z>2.58, we reject the null hypothesis.

Since Z=0.09 is between -2.58 and 2.58, we do not reject the null hypothesis.

So we can not conclude that there is a difference between the output of the two machines.

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Answer: D. A and B are correct

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