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 = 53.0 and a sample standard deviation of s = 5.0. 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 ? = 0.05. Give answers accurate to 3 decimal places.)

Reject H₀ based on the test statistic of 4.02 and a critical value of __________?__________.

Find the critical value.

Answer 1

Here,

Null hypothesis: The average penetration is 50 mils.

Alternate hypothesis: The average penetration is at most 50 mils.

Test Statistic = 4.02

At alpha = 0.05, we conclude that the test statistic > t value for 44 degrees of freedom.

Thus, we reject the null hypothesis and conclude that the average penetration is at most 50 mils.

Reject H0 at a critical value of, say alpha, if and only if test statistic > t value for 44 degrees of freedom at alpha level of signficance.

Thus, the critical value is 0.0005.