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**Unformatted text preview: **A\ r dDM-V(3(U.Ca“ “a \
(uncde memo! Wd’ “xx ST5 2610: Quantitative Methods Spring 2014 ‘2‘, Exercises: Hypothes Tests for p (0 Known) 1. Suppose that previously the average assembly time for the Omega Motors Buzz was 38 hours. The
standard deviation for the process is known to be 3;; _1.2 hours. Modifications have been made to
the process in hopes of reducing the average assembly time. A simple random sample of 35 Buzz
vehicles assembled using the "improved process” have a sample mean assembly time of 37.4 hours.
Assume that the standard deviation for the process remains at 1.2 hours. Does this give statistical
evidence that the changes have reduced the average assembly time. Test using level of significance .05. (\e 35 32 : 31+ 0": 1.2.
m, “M ﬁnpnvt‘mmt-l u isthe owtratﬁ asscmuy NM 0 Ho: Mg 3 5 8
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Test Statistic: 2 = 37' 4" 58 Rejection Region: 16363 2 1- - “:45 , 1
7436 p-value:P 5-39 ': .OQLS .
(2 b) KCICU no 0H as =.o$ Conclusion: i,ng in: average asscmbv Him is rwdrd Give a 95% conﬁdence interval for p. 8y how much has the assembly time been reduced? 2. Following maintenance and calibration, an extrusion machine produces aluminum tubing with mean
2.500 inches. The process standard deviation is 0' 2.027 inches. As the machine functions over an
extended number of work shifts, the standard deviation remains unchanged, but the combination of
accmnulated deposits and mechanical wear causes the mean diameter to drift away from the desired 2.500 inch target value. For a recent random sample of 36 tubes, the mean diameter was 2.509
inches. At level of signiﬁcance .01, is there statistical evidence that the machine needs maintenance andcalibration? nt 35 92‘: 0" = .023
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"ozK'fa'a’o Leveiof significance: 04 7— ,o‘ What is the probabith data will lead us to shut down the process unnecessarily? What type of errorwomdthisbe. ypel rTypeil?
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