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 33 and a sample standard deviation 6 and a sample size of 18. Machine 2 has a sample mean of 31 and a sample standard deviation of 6 with a sample size of 18. 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

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

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

=(33-31)/sqrt(6^2/18+6^2/18)

=1

It is a two-tailed test.

The degree of freedom =n1+n2-2=18+18-2=34

Given a=0.05, the critical values are t(0.025, df=34) =-2.03 or 2.03 (From student t table)

The rejection regions are if t<-2.03 or t>2.03, we reject the null hypothesis.

Since t=1 is between -2.03 and 2.03, 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: B. We will not reject the null hypothesis and thus we can

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