Current technology uses X-rays and lasers for inspection of solder-joint defects

Question

Current technology uses X-rays and lasers for inspection of solder-joint defects on printed circuit boards (PCBs). 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 0.1 inch apart. The equipment was tested by a potential buyer on 48 different PCBs. In each case, the equipment was operated for exactly one second. The number of solder joints inspected on each run is found in the Homework 8.xlsx file, (adapted from [Mendenhall and Sincich 2016], exercise 8.113) a. The potential buyer wants to know whether the sample data refute the manufacturer's claim. Formulate appropriate hypotheses and answer with 95% confidence. b. What is the probability of type II error when the actual population mean is 9 solder joints per second?

Explanation / Answer

a)Testing of hypothesis Ho=10 ag H1 = not Ho

Now here we can perform a t test with sample variance

t=x bar - u/ n*s=9.29-10/48*2.103273= -0.048724

So at level of significance 0.05 ,t 0.05,47=2.01

So statistic t < tabulated t

So we reject null hypothesis...

b)probability of type II error is   (a "false negative")=1/10=0.1

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