Zip, Inc. manufactures Zip drives on two different manufacturing processes. Beca
ID: 3435594 • Letter: Z
Question
Zip, Inc. manufactures Zip drives on two different manufacturing processes. Because the management of this company is interested in determining if process 1 takes less manufacturing time, they selected independent samples from each process. The results of the samples are shown below.
Process 1
Process 2
Sample Size
27
22
Sample Mean (in minutes)
10
14
Sample Variance
16
25
a.
State the null and alternative hypotheses.
b.
Determine the degrees of freedom for the t test.
c.
Compute the test statistic
d.
At 95% confidence, test to determine if there is sufficient evidence to indicate that process 1 takes a significantly shorter time to manufacture the Zip drives.
Process 1
Process 2
Sample Size
27
22
Sample Mean (in minutes)
10
14
Sample Variance
16
25
Explanation / Answer
(a) Let mu1 be the mean for Process 1
Let mu2 be the mean for Process 2
Null hypothesis: mu1=mu2
Alternative hypothesis: mu1<mu2
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(b) The degree of freedom =n1+n2-2=27+22-2 = 47
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(c)test statistic:
t=(xbar1-xbar2)/sqrt(s1^2/n1+s^2/n2)
=(10-14)/sqrt(16/27+25/22)
=-3.04
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(d) It is a left-tailed test.
Given a=0.05, the critical value is t(0.05, df=47) = -1.68 (from student t table)
The rejection region is if t<-1.68, we reject the null hypothesis.
Since t=-3.04 is less than -1.68, we reject the null hypothesis.
So we can conclude that there is sufficient evidence to indicate that process 1 takes a significantly shorter time to manufacture the Zip drives.
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