To obtain information on the corrosion-resistance properties of a certain type o

Question

To obtain information on the corrosion-resistance properties of a certain type of steel codui, edim are buried in soil for a 2-year period. The maximum penetration (in mils) for esch specimen iw t measured, yielding a sample average penetration of 51.8 and a sample standard deviatio of &. h conduits were manufactured with the specification that true average penetralion be at most 50 mil The will be used unless it can be demonstrated conclusively that the specification has not been net (a) (10 pts.) At a significance level of 0.01, is the data sufficient to conclude that the speciicoation ha we been met? Be sure to state the relevant, hypotheses and specify the rejection regiun. (b) (8 pts.) Compute the power of the test if it is really the case that the average peetration o conduits is 52 mils.

Explanation / Answer

a)
Ho : mu = 50
Ha: mu > 50

t = (Xbar - mu)/(sd/sqrt( n))
= (51.8 - 50)/(4.6/sqrt(45))
= 2.624949

critical value for right-tailed test for df = n-1 = 44
is = T.INV(0.99,44)
= 2.414

rejection region
TS > 2.414

since TS > 2.414
we reject the null hypothesis

b)
power = reject the null when it is false
P(Xbar > 50 + 2.414 * 4.6/sqrt(45) | mu = 52)
= P(t > -2 + 2.414 * 4.6/sqrt(45) )
= P(t > -0.344653)
= =1-T.DIST(-0.344653,44,1)
= 0.634001372

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