S1 Hypothesis Testing

Hi all,
Im just a bit confused on the following S1 questions:

"A firm producing mugs has a quality control shceme in which a random sample of 10 mugs from each batch is inspected. For 50 samples, the numbers of defective mugs are as follows:

No. Defetive Mugs No. Samples
0 5
1 13
2 15
3 12
4 4
5 1
6+ 0

It first asks you to find the mean and standard deviation - this I can do.

Then it asks you to show that a reasonable estimate for p, the probability a mug is defective is 0.2 -- I have no idea how to do this part.

Any help?
Thanks :tsr2:

Reply 1

James

Divide the number of defective mugs by the total number of mugs?

Reply 2

King of TSR

How do you know the number of defective mugs, because if you add up the number of samples with one or more defective mugs, then it comes to 90% of the total number.
Could you show the exact calculation if poss.

thanks

Reply 3

James

Think about it. In each of thirteen samples there is one defective mug. So that's 13 defective mugs so far. I each of 15 samples, there are two defective mugs, so that's an additional 30. And so on...

Reply 4

King of TSR

Ah ok so its basically - (sigma "fx") i.e. the mean (which ive already calculated) multiplied by "n". But then if you divide by (50 x (5+13+15+12+4+1), you get 0.04 not 0.2

Reply 5

King of TSR

ahh spotted the error.
Thanks James - absolute genius

Reply 6

King of TSR

How can I use this to work out that the probability of a randomly chosen sample will contain exactly two defective mugs - do I use to binomial distribution, if so, does n =10, r=2, q = 0.2, p = 0.8??

Reply 7

James

Yes, but p=0.2 if X represents the number of defective mugs in a sample.

X\sim B(10,\:0.2)

P(X=2)=\cdots

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