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 null hypothesis? a. the equipment is making the sheet metal too thick. the average steel thickness is greater than 3.416 mm. b. the equipment is not working properly. the average steel thickness is not 3.416 mm. c. the equipment is working properly. the average average steel thickness is 3.416 mm.

Explanation:

Step1: Understand the null hypothesis concept

The null hypothesis (\(H_0\)) is a statement of no difference or no effect. It assumes that the status - quo is true. In the context of testing the thickness of sheet metal, the supposed thickness is \(3.416\) mm. The null hypothesis should assume that the equipment is working as it should (i.e., the average thickness is equal to the supposed value).

Step2: Analyze each option

• Option A: Claims the equipment is making the sheet metal too thick (average thickness is greater than \(3.416\) mm). This is an alternative hypothesis (a claim of a difference from the status - quo), not the null hypothesis.
• Option B: Claims the equipment is not working properly (average thickness is not \(3.416\) mm). This is also an alternative hypothesis.
• Option C: Claims the equipment is working properly (average thickness is \(3.416\) mm). This is in line with the definition of a null hypothesis as it assumes no deviation from the supposed value.

Answer:

C. The equipment is working properly. The average steel thickness is \(3.416\) mm.