3. [10 points] In many manuf as WIP) In a book-manu gathered, each whe a poducti

Question

3. [10 points] In many manuf as WIP) In a book-manu gathered, each whe a poduction plants and the processing time (operationally defined as the time in days from acturing processes, there is a term called work in progress (often abbreviated manufacturing plant, this represents time it takes for sheets from a press to be folded, sewn, tipped on endsheets, and bound. The following data represents samples of 20 books at when the books came off the press to when they were packed in cartons) for these jobs. At 10% significance, is there evidence of a difference between the two plants with respect to average processing time (in days)? Descriptive Statistics: Plant A, Plant Plant A Plant B 9.54 VariableN Mean SE Hean StDev Kinimum 01 Median Plant A 20 09.382.0.894 ).996 4.420 7.343 B.515 11.295 21.620 5.62 .29 16.25 10.92 11.46 25.75 21.62 15.41 14.29 8.58 1.42 10.04 96 4.42 1 13.21 7.58 9.29 7.54 9.71 3.445 5-' d Zx= 1o = ?.on-) $0 m ? tablezd. 64 2 3.1485.13 20 21 1-645 3.013 5.241 From 3 18 Redect Page 4 of 6

Explanation / Answer

x1(bar) = 9.38

x2(bar) = 11.35

s1 = 3.9980

s2 = 5.1300

n1 = 20

n2 = 20

df = 20 - 1 = 19

Null and alternate hypothesis

H0: mu(A) - mu(B) = 0

H1: mu(A) - mu(B) not equals to 0

SE = sqrt[ (s12/n1) + (s22/n2) ]

(s12/n1) = 0.7992

(s22/n2) = 1.3158

SE = 1.4543

Test statistics,

t = [ (x1 - x2) - d ] / SE

t = (9.38 - 11.35)/1.4543

t = -1.3532

p-value = 0.1919

As p-value is greater than the significance level of 0.1, we fail to reject the null hypothesis.

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