The following table describe the relationship between computer networking equipm

Question

The following table describe the relationship between computer networking equipment failure and the ambient temperature in which the equipment is operated (this was recorded as low, median or high temperature). A technician randomly selected 250 pieces of networking equipment and the following. Suppose we wish to test H_0: temperature and failure are independent versus H_: temperature and failure are not independent at the alpha = 0.10 significance level. Which of the following is/are true? (a) The p-value for this test is in the interval (0.05, 0.10) (b) e_22 = 25.2 (c) We have evidence that temperature and failure are not independent. (d) The probability of failure for equipment in low operating temperature is 0.089. (e) All of the above.

Explanation / Answer

a) p value =0.0385 --false

b)e23=25.2 --true

c)true

d)probabilty =8/250=0.032 --false

e)false

Observed O low temp Med temp high temp Total failure 8 24 8 40 no failure 82 106 22 210 Total 90 130 30 250 Expected E=rowtotal*column total/grand total low temp Med temp high temp Total failure 14.400 20.800 4.800 40 no failure 75.600 109.200 25.200 210 Total 90 130 30 250 chi square =(O-E)^2/E low temp Med temp high temp Total failure 2.844 0.4923 2.1333 5.470 no failure 0.542 0.094 0.406 1.042 Total 3.386 0.586 2.540 6.5120

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