Question

a sheet metal manufacturer is making 10 - gauge sheet metal, which is supposed to be 3.416 mm thick. one of the pieces of manufacturing equipment was suspected of malfunctioning, so the manufacturer tested a random sample of 100 pieces of steel to make sure the average steel thickness is 3.416 mm. which of the following is a statement of the alternative hypothesis?
a. the equipment is making the sheet metal too thick. the average average steel thickness is greater than 3.416 mm.
b. the equipment is working properly. the average average steel thickness is 3.416 mm.
c. the equipment is not working properly. the average average steel thickness is not 3.416 mm.

Explanation:

In hypothesis testing, the alternative hypothesis ($H_1$) is what we are trying to find evidence for. The null hypothesis ($H_0$) is the statement of no effect or no difference. Here, the null hypothesis would be that the average steel thickness is 3.416 mm (i.e., the equipment is working properly). The alternative hypothesis is the opposite of the null hypothesis. Option C is the alternative hypothesis as it negates the claim that the average thickness is 3.416 mm (implying the equipment is not working properly). Option A is a one - sided claim (greater than) which is not indicated by the problem (the problem just suspects malfunction, not specifically over - production). Option B is the null hypothesis.

Answer:

C. The equipment is not working properly. The average average steel thickness is not 3.416 mm.