statistics A2 level: post doubts here

[shanky631]

Hello friends, feel free to post ur doubts, answers, or any other valuable resources related to A2 statistics. Together as a team we may increase our probability of scoring A+. So plz let's help out each other!!!

Thanks

 

[parthrocks]

Hey I have a doubt I am posting it here asap!!

 

[parthrocks]

Hello friends, feel free to post ur doubts, answers, or any other valuable resources related to A2 statistics. Together as a team we may increase our probability of scoring A+. So plz let's help out each other!!!

Thanks

http://www.xtremepapers.com/papers/...AS Level/Mathematics (9709)/9709_s07_qp_7.pdf
doubt in question number 5....help...plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

 

[shanky631]

does anyone have good notes for S2??

 

[shanky631]

do we do addition of probabilities to find rejection area in binomial distribution too???

 

[parthrocks]

do we do addition of probabilities to find rejection area in binomial distribution too???

Ya offcourse there are many questions in the past papers!!the simplistic dealing of critical values of a sign change!

 

[shanky631]

Ya offcourse there are many questions in the past papers!!the simplistic dealing of critical values of a sign change!

and in two tail, we also have calculate from backward?

 

[parthrocks]

and in two tail, we also have calculate from backward?

didnt get you!!matlab

 

[parthrocks]

and in two tail, we also have calculate from backward?

Its given in the statistics 2 textbook!

 

[parthrocks]

Ya offcourse there are many questions in the past papers!!the simplistic dealing of critical values of a sign change!

like!?

 

[parthrocks]

Can someone help me with this
help with a bit explanation

shanky631
Vinita Manek

 

[Ranzis]

Can someone help me with this
help with a bit explanation
View attachment 17953
shanky631
Vinita Manek

Type 1 error is the probability of rejecting a null hypothesis when it is actually true.
So in this example here, using reference to the situation, you'd say that:
Type 1 error is the probability that you reject the claim that it is 20% red for sugar-coated chocolate beans when they actually are 20%.

 

[shanky631]

Type 1 error is the probability of rejecting a null hypothesis when it is actually true.
So in this example here, using reference to the situation, you'd say that:
Type 1 error is the probability that you reject the claim that it is 20% red for sugar-coated chocolate beans when they actually are 20%.

can u help me with this

 

[Ranzis]

can u help me with this
View attachment 17956

For this you need to realise that these are discrete values.
The Type I error is at most 0.1.
Null hypothesis is when p = 0.5.
Alternative hypothesis is p does not equal to 0.5. Therefore this is a two tailed test.

X~B(10, 0.5)
P(X=0) = 0.000976562
P(X=1) = 0.009765625
P(X=2) = 0.0439453125

Since it is two tailed, we are calculating up to 0.05.
To find the acceptance region for the test, we need to find what values of x do not fall into the rejection region.
P(X=0) is lower than 0.05.
P(X=<1) is lower than 0.05 (add P(X=1) and P(X=0) together.
but P(X=<2) is higher than 0.05. This means that when X=<2 it is not rejected as being not biased to a 0.1 significance level.

Therefore the acceptance region of the test would be P(X=>2), as any values below that fall into the rejection region.

For the second part of calculating a Type II error.
Type II error is the probability of accepting the null hypothesis when it is actually false.
Ignore that 'when it is actually false part', it always confused me. Just calculate the probability of accepting the null hypothesis, ie. not in the rejection region. The rejection region was P(X<2).
So the acceptance region for accepting the null hypothesis is P(X=>2).

Using the new probability, X~B(10, 0.7), calculate P(X=>2).
ie. 1 - P(x<2), which is 1- P(X=1) - P(X=0)
=0.9998563141 = 1.00.
Okay, something's wrong here.
What paper was this and the question?
I probably made a error in calculation somewhere.

 

[shanky631]

 

[Ranzis]

Oh damn. I forgot that since it was two tailed, you'd account for the other end of the spectrum as well...

Well the working that I did above still holds.
I did it for two tailed, so that the probability would be less than 0.05 on one side.
Which is still the values of 0 and 1.
Then you need to account for the other side of the two tailed test, 9 and 10.
This makes the acceptance region 2<= X <= 8

So then the Type 2 error is everything within that region, since thats the probability of accepting the null hypothesis.
So that's 1- P(x=0) - P(X=1) - p(X=9) - P(X=10)
which is 1 - 0.149 using X~B (10,0.7)
= 0.851.

 

[shanky631]

Oh damn. I forgot that since it was two tailed, you'd account for the other end of the spectrum as well...

okay, so we don't compare with half of 10% then, right??

 

[Ranzis]

okay, so we don't compare with half of 10% then, right??

The thing is that you can. They're using 10%, but finding the probability of P(X=1) and then doubling it to account for P(X=9) and likewise for the other probabilities. You could do that, or you could just focus on one side and half it to 5%.

I'll hang around here for most of the time until before the exam.
If you need any help just post here, I'll probably see it.
Helps me to revise myself.

 

[parthrocks]

Type 1 error is the probability of rejecting a null hypothesis when it is actually true.
So in this example here, using reference to the situation, you'd say that:
Type 1 error is the probability that you reject the claim that it is 20% red for sugar-coated chocolate beans when they actually are 20%.

Hey bro m posting my doubts can u help me plz!??

 

[shanky631]