Question

Solder-joint inspections. Current technology uses high-resolution X-rays and lasers to inspect solder-joint defects on printed circuit boards (PCBs) (Global SMT & Packaging, April 2008). A particular manufacturer of laser-based inspection equipment claims that its product can inspect, on average, at least 10 solder joints per second when the joints are spaced .1 inch apart. The equipment was tested by a potential buyer on 48 different PCBs. In each case, the equipment was operated for exactly 1 second. The number of solder joints inspected on each run follows:

The potential buyer wants to know whether the sample data refute the manufacturer’s claim. Specify the null and alternative hypotheses that the buyer should test.

Short answer

a. The null and the alternative hypotheses are \({H_0}:\mu \ge 10\)and \({H_a}:\mu < 10\)

Step-by-step solution

Given information

The data of equipment tested by a potential buyer on 48 different PCBs are as follows:

Specifying the null hypothesis

Null hypothesis:

\({H_0}:\mu \ge 10\)

That is, the mean inspection rate is 10 soldier joints per second.

Specifying the alternative hypothesis

Alternative hypothesis:

\({H_a}:\mu < 10\)

That is, the mean inspection rate is at least 10 soldier joints per second.