Question

To obtain information on the corrosion-resistance properties of a certain type of steel conduit, 45 specimens are buried in soil for a 2-year period. The maximum penetration (in mils) for each specimen is then measured, yielding a sample average penetration of x 5 52.7 and a sample standard deviation of s 5 4.8. The conduits were manufactured with the specification that true average penetration be at most 50 mils. They will be used unless it can be demonstrated conclusively that the specification has not been met. What would you conclude?

(a) Answer the question as stated. Test whether the true average penetration is greater than 50 mils. That is that the specification has not been met

(b) Carry out the test using P-value Method. It’s not necessary to repeat steps 1), 2), 3)

(c) Considering the H 0 and H a for this test, describe specifically the possible Type I error and the possible Type II error.

(d) Considering the conclusion for the test, which one of the two errors could have occurred?

Answer 1

n = 45

= 52.7

s = 4.8

= 50

A and B.

H₀: 50

H₁: > 50

z = ( - )/s/

= (52.7 - 50)*/4.8

= 3.77

p-value =  0.000082 < 0.05 () i.e. H₀ is rejected and hence we can say that specifications have not been met.

C.

Type 1 error: It occurs when the null hypothesis (H₀) is true but is rejected that is in this case if actually specifications were met and we concluded that they are not.

Type 2 error: It occurs when the null hypothesis is false, but erroneously fails to be rejected that is in this case if actually specifications were not met but we conclude that they are.

D.

Looking at the conclusion we can say that we may have committed type 1 error because we have rejected the null hypothesis which could have been true.

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