Show all work please Show all work please Homework #4-Chapter13 (20pts for turne
ID: 3049837 • Letter: S
Question
Show all work please Show all work please Homework #4-Chapter13 (20pts for turned in on time) 9. (11pts) Here we will introduce the idea of hypothesis test If you see an event, which has a very low chance to occur, by assuming a condition is TRUE, it will lead to a conclusion that the assumption is FALSE In this example: If we ASSUME it is TRUE that the probability of one piston is bad is 0.05 then we can find out the probability of 3 or more out of 10 pistons are bad. From calculation, this is a very low probability event. If we randomly select 10 pistons, and observe that low probability event, it will prove the ASSUMPTION we had is FALSE. The ASSUMPTION is called NULL HYPOTHESIS The probability calculated is called P-VALUE with observed count of 3. A manufacturer of metal pistons claims that on average, only 5% of their pistons are bad either oversize or undersize). When the pistons are delivered to a local store, a quality control staff will randomly select 10 pistons, and measure out if they are oversize or undersize. If he sees 3 or more pistons are bad, they will reject the delivery What is the probability that 3 or more of those randomly selected 10 pistons are bad, if we assume the fault rate for the pistons is 0.05? (Hint: Define variable x = # of pistons that are either oversize or undersize out of those 10 pistons, what distribution will X have? Complement Rule: P (Not A)- 1-P (A) From Complement Rule: P(X23) 1-P(XExplanation / Answer
X= number of pistons that are either over sized or under sized.
X follows binomial distribution
here, n= 10
p = probability that the pistons are either oversized or undersized = 0.05
P[X=x] = nCx px (1-p)n-x
P [ X >=3 ] = 1-P [ X=0]-P[X=1]-P[X=2]
= 0.01150355738