Discussion in 'Mathematics' started by ian60, Apr 17, 2012.

1. ### ian60New commenter

Summarising a question in the text that I use for IB HL Stats Option:
• Six coins are tossed loads of times, no. of tails recorded
• At least one tail appears on each occasion
• Observer concludes that one of the coins is TT, while the others are fair.
State the null and alternate hypothesis to test this assertion.
What would be your H0 and Ha?
(And noone is allowed to make any HoHoHo, HaHaHa jokes)

H0 - distribution is B(6,0.5). Ha - one of the coins is TT.

The probability of getting no tails is 0.015625, which you might then use as another binomial distribution with N being your "loads of times", and then see if getting no tails no times falls in the critical region.

I'm sure there are other approaches as well, which others might suggest.

3. ### ian60New commenter

I would have said the same thing, however my book uses H0: One of the coins is TT, which I found a little strange as I always try to use the 'No change' approach.

Out of curiosity, what book are you using? I too, and I think most books, teach that the null hypothesis preserves the status quo. Did the question simply ask for the hypothesis, or did it also go on to show a test, because I'd be interested to see how a test from this angle could be done as it would be impossible not to get a result with a tail.

Perhaps some others might like to add their opinion to this thread.

5. ### Polecat

My understanding is that hypothesis testing is about investigating
a claim made by someone. The null hypothesis is that claim.
So I agree with the answer given in the book.
Someone else might make the claim that all of the 6 coins are
fair - I think this is what Ian and David mean by 'no change' and
'status quo' - but that is not what the claimant said in the question.

6. ### ian60New commenter

Really Polecat?! I often tie myself up in knots trying to unravel these things.
So if a politician claimed he had more support than a rival, and a poll was taken, your H0 would be that the politician did have more support. And your Ha would be that he did not have more support?
I have always thought that an H0 tests that a parameter is <u>equal</u> to a value, and that Ha is either it is not equal, (or greater than/less than) that value.
(The text book is Haese & Harris Maths HL (Options))

7. ### Polecat

A value for a parameter is not always stated in either hypothesis. For example, one might think that a particular distribution, representing the results of a repeated experinent, looked binomial, but did not have a strong view about the value of the parameter p. If one wanted to test this using chi-squared, then
H_0: The distribution is binomial. H_1: The distribution is not binomial.
Estimate a value of p from the observed data and use it to calculate the expected data. Then go through the chi-squared routine, at one's favourite significance level, remembering to subtract an extra one from the number of degrees of freedom - this is because the p used was esrtimated rather than being part of the null hypothesis.
I have found the question in H&H. Fine, except I would have omitted the last word in the solution - statistics never proves anything!

8. ### Polecat

I've just remembered that for Q3 in the May 2012 stats option paper the correct hypotheses did not involve a parameter value. In fact, for stating a parameter value, candidates were rewarded with the loss of a mark.

9. ### ian60New commenter

I would be very interested in looking at the May 2012 option paper, if you could just discretely pass one over this way
Thanks very much for explaining your understanding. I reallly appreciate it.

10. ### Polecat

I had a memory of marking such a question a few Summers ago, I think it must have been May09, because that is the only one I can't find on my system.

I've just looked up the question.

It actually gives the number of trials as 275 AND a frequency table; it also says that as well as concluding one TT the rest of the coins are assumed to be fair.

With all this, the book's hypothesis is the correct one since we are doing a Chi Squared test of a specific model.

By the way, what are people's feelings on Chi Squared being dropped? It appears that the IBO decided that bivariate analysis was a more appropriate topic.

12. ### KarvolOccasional commenter

As a department, we tend to teach either Sets and Relations or Discrete, so not a great concern.
We are more concerned about there being no more matrices, but the students still being expected to learn row reduction methods. This has meant that we are now teaching a large part of the IB HL Matrices option in the pre-IB year to the classes that would be interested in taking HL.