Part B is where I\'m stuck. Please show all work. 2. System data for the job sho
ID: 3365027 • Letter: P
Question
Part B is where I'm stuck. Please show all work.
2. System data for the job shop of Exercise 1 revealed that the average time spent by a job in the shop was approximately 4 working days. The model made the following predictions, on seven 3.70 4.21 4.35 4.13 3.83 4.32 4.05 (a) Is model output consistent with system behavior? Conduct a statistical test, using the level of (b) If it is important to detect a difference of 0.5 day, what sample size is needed to have a power independent replications, for average time spent in the shop: significance -0.01. of 0.90? Interpret your results in terms of model validity or invalidity. (Use = 0.01)Explanation / Answer
2.Solution:
a) We assume = 4. Conduct a t-test using the 7 values against the mean (using the TTEST function in EXCEL), revealing an answer of 0.38398. Using the TINV function on this value with 6 degrees of freedom, we get the t-value = 0.913476. Since our a level of significance is 0.01, we use the TINV function on this value with 6 degrees of freedom to get the critical value in this case = 3.7074. Since our t-value is well under the critical value, we do not reject the null hypothesis.
Note that this problem could also be solved using the formulas in the text, in the following fashion:
Y_bar = 4.08 Sy = 0.2441 (using the formulas on p. 369 of the text)
From this we can use Equation 10.2 to get t0 = (Y_bar – )/(Sy/n1/2) = (4.084 – 4)/(0.2441/71/2) = 0.91. The rest of the answer is the same as above.
b) Sample size:
For 0.01 level, z = 2.576
d = 0.5
standard deviation s = 0.2441
for =0.10, z =1.282
n = (Z + Z)2 * s2/d2
= (2.576 + 1.282)2 * 0.24412
= 3.1
The required sample size = 4