The Edexcel S2 (24/05/12 - AM) Revision Thread

Part C if this, right?
During a single game, a player receives 12 “balls”.
(c) Find the probability that the ball appears within 3 cm of the middle of the top edge of the playing area more than four times in a single game?

Basically, it forms a binomial distibution of X~B(12,0.25) the 0.25 being worked out from part b. Then you just do P(X>4)

Anyone know if answers are guna be up online after exam next day?

Sorry missed your post, the proof is on page 72 of the new textbook. Let me know if you can't find it i'll link it to you.

I would like to know this as well. Gibbo is usually the one to do S2 solutions but I dont know if he'll be doing them this time.

I'll upload the paper so we can make solutions if no one's going to do them, thats if i manage to get a copy (most likely will).

Thank you, just took a look now, didn't really follow it, but how on earth is the E(X^2) - E(X)^2 way more difficult than that?

Can anyone post or PM me June 2011 and Jan 2012 papers and mark schemes? Would really appreciate it.

I would like to know this as well. Gibbo is usually the one to do S2 solutions but I dont know if he'll be doing them this time.

I'll upload the paper so we can make solutions if no one's going to do them, thats if i manage to get a copy (most likely will).

I'm happy to contribute if someone can get the paper uploaded.

I'm happy to contribute if someone can get the paper uploaded.

I will be happy to try to do the solutions if someone can get me the paper.

Can you get a copy of FP2 and FP3 as well?

If I do get the paper, i'll pm it you so solutions can be ready at midnight on the day, when we're allowed to discuss .

I will be happy to try to do the solutions if someone can get me the paper.

Can you get a copy of FP2 and FP3 as well?

If I do get the paper, i'll pm it you so solutions can be ready at midnight on the day, when we're allowed to discuss .

I PMed Gibbo81 and he said will be doing the solutions for S2 so no need to worry guys.

No one in my college is doing FP3, and my last exam is before FP2 so I wont be in college to get a paper.

I'll pm S2 to you if i get a copy.

Can't someone in your school get the FP2 paper and send it to you?

There's only one person doing it and I dont know them. Sorry.

Doesn't Gibbo do FP2?

There's only one person doing it and I dont know them. Sorry.

Doesn't Gibbo do FP2?

Hypothesis testing is basically where you'll test a hypothesis based on what the probability of that thing happening is by chance.

If I claim to have magical powers so I can guess what side of a dice will come up at any given roll, we can test to see if this is likely, or if I'm just fibbing.

For this, we'll make two hypotheses; for if I'm fibbing, because I don't have any magical powers. This will be called the Null Hypothesis - what we are testing for isn't true. There will be another hypothesis which is called the Alternate Hypothesis which basically means that something is out of the ordinary. We are testing to see which hypothesis is true.

The way we do this is by setting a 'level of significance" which is a percentage chance and tells us how rigorous our test will be. It is usually around 5%. In other words, if we do a test of 50 goes, and I guess 35/50 correctly (you are able to find out what the probability of getting 35/50 dice rolls is), the probability of this happening purely by chance must be less than the level of significance - ie. if the set level of significance is 5% and the chance of me getting 35/50 rolls guessed correctly by chance (under the Null Hyposthesis) is only 4%, then we can likely assume that I have supernatural powers and reject the Null Hypothesis and accept the Alternate Hypothesis. If the probability of me guessing 35/50 correctly is something like 14%, then we can likely assume that I'm fibbing and just playing on chance rather than my magical powers and we accept the Null Hypothesis and reject the Alternate Hypothesis.

The set of results in which we accept the Alternate Hypothesis is called the Critical Region. In our example, with a 5% level of significance, we might be able to say that the critical region is X > 45, so basically saying that if the number I guess correctly is 45/50 or above, then I will be trusted as having magical powers.

That is a one-tailed test. This means that only one end is important (ie. the critical region is only in the top end of the number I can get right.)

If for example we were talking about finding whether a machine that cuts bars of set lengths is faulty of not (doesn't cut the right length), we might use a two-tailed test. So saying that if the average length of the bars is under 45.5cm and above 55.5cm, then we can say that the machine is not cutting them correctly. Therefore, the critical region would be both at the top end and the bottom end - a two-tailed test.

In questions - they'll most likely give you a set level of significance at 5%, and tell you that I roll 35/50 correctly. Then they'll probably just ask you whether I have magical powers or not, stating your Hypotheses clearly. We know that Binomially, the chance of me getting one right is p = 1/6;

- p = 1/6
- p > 1/6

so saying that if I do have magical powers, the chance of me getting one right is larger than 1/6.

To find out which one we accept, you should look in your tables, for a binomial distribution of B(n,p) where n = 50 and p = 1/6, and find that indeed if I were to get 35 right, what the cumulative probability of that is. If the cumulative probability of 35/50 is 0.9400, then that leaves 6% chance that I will get above 35/50 right. This is greater than our level of significance so we reject the Alternate Hypothesis.
If on the other hand, the cumulative probability of 35/50 is 0.9999, then we can tell that the chance of me getting 35/50 is so slim, that I'm probably telling the truth, so we accept the Alternate Hypothesis.





That, in a nutshell, is Hypothesis Testing. If you need to ask me anything else, just quote me in this thread or PM me or something, I'd be glad to help