The qualitycontrol inspector of a production plant is in cha

The quality-control inspector of a production plant is in charge inspecting gadgets. His job is to make sure that the production machines are working properly. Each day he randomly selects gadgets to inspect and if there is evidence that more than 10% of gadgets are defective then he must put in a work order for the production machines to be fixed. Today he was really pressed for time and only selected 5 gadgets to inspect. Out of the 5 he inspected, 3 of them were found to be defective.

a) What is the random variable? Explain why this random variable has a binomial distribution.

b) State the null and alternative hypotheses in statistical notation. Define any notation used.

c) What is the expected number defective gadgets? (Find the expected value for this binomial random variable) Show all work. If the null hypothesis is true, what counts are considered “as or more unusual” than the observed count.

d) Calculate the p-value using the binomial formula. Is there any evidence that the machines are producing more than 10% defective gadgets?

Solution