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 = 53.4 and a sample standard deviation of s = 4.4. 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? (Use α = 0.05.) State the appropriate null and alternative hypotheses.

Answer 1

Explanation:

Set up hypotheses as

`H_0: x bar = 50\\H_a: x bar <50`

(Left tailed test at 5% level)

Sample mean = 53.4

Sample std dev s = 4.4

Sample std error = 4.4/sqrt 50 = 0.6222

Mean diff = 3.4

Test statistic = Mean diff/std error = 0.5464

(t test only can be used as population sigma is not known)

df = 50-1 =49

p value = 0.2939

Since p>0.05 we accept null hypothesis

Specification has not been met.