Question

In many manufacturing processes, the term work-in-process (often abbreviated WIP) is used. At BLK publishing book manufacturing plants, WIP represents the time it takes for sheets from a press to be folded, gathered, sewn, tipped on end sheets, and bound together to form a book, and the book placed in a packing carton. The operational definition of the variable of interest, processing time, is the number of days (measured in hundredths) from when the sheets came off the press to when the book is placed in the packing carton. The data below represent samples of WIP times for 20 books at each of two manufacturing plants, Plant 1 and Plant 2. NOTE: You can copy and paste the data into Excel/PHStat. The manager of Plant 1 claims that his WIP time is lower than the WIP time at Plant 2.

Plant 1
5.62
5.29
16.25
10.92
11.46
21.62
8.45
8.58
5.41
11.42
11.62
7.29
7.5
7.96
4.42
10.5
7.58
9.29
7.54
8.92

Plant 2
9.54
11.46
16.62
12.62
25.75
15.41
14.29
13.13
13.71
10.04
5.75
12.46
9.17
13.21
6
2.33
14.25
5.37
6.25
9.71


a. Construct a 99% confidence interval estimate for the mean WIP time at Plant 1.
7.14 - 11.62
b. Construct a 99% confidence interval estimate for the mean WIP time at Plant 2.
8.47649-14.23051
c. Do the results of parts (a) and (b) support the claim made by the manager of Plant 1? Explain your answer.
d. What must be true about the data sets to make the confidence intervals you constructed in parts (a) and (b) valid?

Answer 1

Answer and step -by-step explanation:

a) estimate with 99% confidence interval plant 1

Middle Floor 1 = 9,417

Standard Deviation = 4,979

Given alpha = 1 - (. 99) = .01

Z = 2,045

CI = Average +/- (Z * SD / sqrt (n))

the result is:

CI = 7.14 to 11.62

b) estimate with 99% confidence interval plant 1

Plant mean 2 = 11,353

Standard deviation = 6.293

Given alpha = 1 - (. 99) = .01

Z = 2,045

CI = Average +/- (Z * SD / sqrt (n))

Outcome:

CI = 8.47 to 14.23

c) Yes, they are compatible because the IC is lower for both limits in Plant 1 than in Plant 2

d) it must be true that the confidence intervals between wider, will have less probability of error and more success, however when this is very small the possibility of error will also increase