Question

In: Statistics and Probability

The costs (in millions) of 26 construction projects at a large industrial facility are given below....

The costs (in millions) of 26 construction projects at a large industrial facility are given below.

0.707 0.918 1.143 1.240 1.553 2.003 3 .692 4.069 4.324 5.292 7.214 7.642 10.523 13.371 14.577 14.837 15.317 15.320 20.099 21.571 27.973 29.522 30.028 34.100 38.173 51.284

Is there sufficient evidence to conclude that the median cost for construction projects at this facility is under 20 million dollars? (α = 0.05)

Solutions

Expert Solution

Sign Test:

H0: The median cost for construction projects at this facility is not under 20 million dollars

H1: The median cost for construction projects at this facility is under 20 million dollars

Let the los be alpha = 5%

From the given data

S.No. X X-Median
1 0.707 -19.293
2 0.918 -19.082
3 1.143 -18.857
4 1.24 -18.76
5 1.553 -18.447
6 2.003 -17.997
7 3.692 -16.308
8 4.069 -15.931
9 4.324 -15.676
10 5.292 -14.708
11 7.2147 -12.7853
12 7.642 -12.358
13 10.523 -9.477
14 13.371 -6.629
15 14.577 -5.423
16 14.837 -5.163
17 15.317 -4.683
18 15.32 -4.68
19 20.099 0.099
20 21.571 1.571
21 27.973 7.973
22 29.522 9.522
23 30.028 10.028
24 34.1 14.1
25 38.173 18.173
26 51.284

31.284

The number of positive signs S+ = 18

The number of negative signs S- = 8

Thus we conclude that the median cost for construction projects at this facility is not under 20 million dollars

orchestra answered 1 year ago
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