14 The article Thermal Endurance of Pol Enameled Wires Using

14. The article \"Thermal Endurance of Pol Enameled Wires Using Twisted Wire s Reiter by H. Goldenberg (IEEE Transactions on E cal Insulation, 1965) contains some data on the lifetimes (in weeks) of specimens thermal endurance according to AIEE start 57. Several different laboratories were used to make the tests, and the results from two of the laboratories, using a test temperature of 200 c follow: Laboratory 2 Laboratory 1 14, 16, 17, 18, 20, 27, 28, 29, 29, 29, 22, 23, 25, 27, 28 30, 31, 31, 33. 34 Consider first only the Laboratory 1 data. (a) Find the median and the first and third quar- tiles for the lifetimes and then find the 64 quantile of the data set. (b) Make and interpret a normal plot for these data. Would you describe this distribution as bell-shaped? If not, in what way(s) does it depart from being bell-shaped? Give the co ordinates of the 10 points you plot on regular graph paper. (c) Find the sample mean, the sample range, and the sample standard deviation for these data Now comparing the work of the two ferent laboratories (ie, consider both sets. data

Solution

1) 1st sample median = 21

1st quartile = 16.75

3rd quartile = 25.5

2) Normal probability plot of the 1st sample

as p-value = 0.881 > 0.05 the sample is normally distributed and hence, bell shaped

c) Sample mean = 21, Range = 28 -14 = 14, Std.dev = 4.78

d)

Stem-and-Leaf Display: of 1st and 2nd lab sample data

Stem-and-leaf of 1st sample N = 10
Leaf Unit = 1.0

1 1 4
3 1 67
4 1 8
5 2 0
5 2 23
3 2 5
2 2 7
1 2 8

Stem-and-leaf of 2nd sample N = 10
Leaf Unit = 0.10
N* = 1

1 27 0
2 28 0
5 29 000
5 30 0
4 31 00
2 32
2 33 0
1 34 0

e) Box plot of 2 samples

e) From the two plots I would say that 2nd sample produce more precise results as values are more close to each other and there is lless variance

f) No it is not possible to tell which sample produce more accurate result as there is no value to compare in order to obtain accuracy of the sample