For the job shop of Exercise 1, four sets of input data were collected over four
ID: 3180994 • Letter: F
Question
For the job shop of Exercise 1, four sets of input data were collected over four different 10-day periods, together with the average number of jobs in the shop Zi for each period. The input data were used to drive the simulation model for four runs of 10 days each, and model predictions of average number of jobs in the shop Yi were collected, with these results: (a) Conduct a statistical test to check the consistency of system output and model output. Use the level of significance a = 0.05. (b) If a difference of two jobs is viewed as important to detect, what sample size is required to guarantee a probability of at least 0.80 of detecting this difference, if it indeed exists? (Use a =0.05.)Explanation / Answer
(a) We carry out a paired t-test to see if we have consistency of system output and model output. The test is performed in R softward:
> z <- c(21.7,19.2,22.8,19.4)
> y <- c(24.6,21.1,19.7,24.9)
> t.test(z,y,paired=TRUE,var.equal=TRUE)
Paired t-test
data: z and y
t = -0.99949, df = 3, p-value = 0.3912
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-7.531349 3.931349
sample estimates:
mean of the differences
-1.8
Since the p-value is large, at 0.05 level of significance, we conclude that the system output and model output are same.
(b) Since the difference is insignificant, we don't have to evaluate the sample size calculations.