S2 18th January 2013

Well assuming that the value if y is always greater than 1

For working out the P(X=x) would you get full marks for using the formula?

Speaking from an OCR experience, yes.
You may also be required to add together P(x< or = n) for small n for full marks too, such as :

P(X=1) = P(X=0) + P(X=1)

But don't quote me on that.

You mean P(X=<1)

In these cases it should be very obvious which method to take.

Yes, I know, but my issue is with all numbers. You can't just ignore y < 1 and say that it holds

Can you see an actual flaw with the argument?

if a^x < b, and we take log[y]

then log[y](a^x) < log[y](b)

and xlog[y](a) < log[y](b)

if y is such that log[y](a) < 0
then x > log[y](b) / log[y](a)
and x > log[a](b) by the law of logs.

if y is such that log[y](a) is not < 0
then x < log[y](b) / log[y](a)
and x < log[a](b) by the same law.

so if a^x < b then x (> or <) log[x](b), with the inequality determined by the chosen value of y. Therefore there are either two solutions to every log inequality, or there's a mistake somewhere in that logic.

H1 > 0.5 as the local radio forecast got the unexpected result of 21/30 correct results, which is more than the expected 15. Therefore you test that H1 > 0.5 as that is what the data shows... If they got less than 15 correct answers it would be < 0.5

First of all before I go any further the first mistake you are making is that

loga / logb = log(a/b)

is the expected value of a pdf always the mode?

This question seems to have shaken my confidence in hypothesis testing.

What do you mean expected value?

is the expected value of a pdf always the mode?

First of all before I go any further the first mistake you are making is that
loga / logb = log(a/b)
this rule only applies to loga-logb
Follow this rule and then you'll see that you are totally incorrect.

I never made this mistake. Look again and you'll see I used the change of base law, not subtraction.

Hey there, please could someone tell me when we have to work out the critical region are we required to put x is between the limit and the number, for example if it was a binomial distribution with a sample of 20 and the critical value was 16. Is it okay to put x greater than or equal to 16 as the critical region or does it need to be between 16 and 20.
Also if the lower tail was 0 would the critical region just be x=0

E(X) aka the mean

Ok sorry for that but still considering 8^x = 16


xlog8=log16
x=log16/log8 = log8(16)

now with your assumption that if log[y]a is <0

so xlog(0.5)8=log(0.5)16
x=log(0.5)16/log(0.5)8 = log(8)16

both operations lead to the same result.

probability of rejecting H0 when H0 is true,
which is the same as the probability of incorrectly rejecting H0.

Yes, X >= 16 is fine and so is X = 0. In fact I think those are the answers they would expect you to give in these situations, as they are on all the Edexcel Mark Schemes.