Homework SourseYou want to determine if your widgets from machine 1 are the
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 |
Solution
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
