26. 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-bar= 52.7 and a sample standard deviation of s = 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?
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Solution. Denote the population penetration by . We can set up the null and alternative hypotheses as follows.
Now a sample was ...
Hypothesis testing, mean and standard deviation are investigated and discussed. The solution is detailed and well presented.