I'm having difficulty answering the essay" statistics questions I keep encountering in my practical work. Here are questions and answers in particular:
A manufacturer buys many thousands of a particular component and has agreed with the supplier that only 1% should be defective. To check the quality of a particular batch of components, the manufacturers take a random sample of 25 and thoroughly test them.
i) They find out that two in the sample are defective. If it is true that only 1% of the supplier's output of these components is defective, what is the probability of this happening?
1% of 25 = 0.25
P(r =2) = ${}^{25}C_2$ * 0.25$^2$ * 0.75$^{23}$ = 0.03
This is question I am having difficulty answering. The value of 0.03 obtained in i) seems correct but how would I tackle the below question?
ii) You will now need to consider how you will react to your findings in part (i). There will be variation, between sample size samples, in the number defective if these samples are randomly selected. The probability you calculated tells you how likely it is that you could exactly two defective components out of a randomly selected sample of 25 if, and only if 1% of the output is defective.
In this particular case, would you consider an event with a probability of 0.05 or less to be "unusual", and therefore requiring action, or would you go for a different cut off point? Accordingly, how would you interpret the probability calculated in part (i)? Other than the statistics, what else might you take into consideration? Finally what action would you take if any?
Thanks in advance!