Binomial Distribution

Question 1

How to do hypothesis test 1 tail

Answer 1

Let p be lrobablity
Let x be the nunber of people

H0 =
H1=

Significance level set at 5% or whatever

If H0 is true, x follows BD between (N,p)

P (X<…) =
TEST FOR EXTREME

Now say o value is less or higher

If higher don’t reject if less then it’s too low to happen by chance , so reject
THERE IS INSUFFIEMCT EVIDECNCE AT THE 5% LEVEL

Question 2

Remember for null hypothesis snd alternstive

Answer 2

DONT PUT DOWN PERCENTAGES

Question 3

How to find out if H1nhas increased or gone less

Answer 3

Multiply probability with value to find expected. If now values Is lower or higher you know

Question 4

What errors can iccure with significance levels?
2 ERRORS TAKE HEED

Answer 4

There could be an error where H0 is correct, but because significance level too high, you reject it anyways

The probability if making this error is EQUAL TO SIGNIFICANCE, t

Thus the lower the significance level the better

2) another error is where you reject H0 when yiu should not, again the higher the significance level you increase this

Question 5

Don’t say certain always say

Answer 5

Insufficent

Question 6

What happens if you take a larger data set for same success

Answer 6

It is likely that outcome changes, normally if it is not rejected then it might be rejected, a larger dats set Leeds to better results (more conclusive

Question 7

Okay how to do critical region tests

Answer 7

Basically same as before

Let p be
Let x Be

H0 is
H1 is

Now if Yiu are testing for a higher extreme then finding P (x>=a) <0.05 the lowest value for a
Which is 1 - p (x<=a-1) <0.05
0.95< p
So find highest value that still satisfies this situation
A-1 = that
And so 1 = that +1

So now yiu have a critical region

And if observed value falls in it then reject

If not do not reject

Question 8

When can a critical region NOT BE ESTABLISHED

Answer 8

If yiu are testing for x < 0 then Yh it can’t be because if x=0 is already likely then there is no critical region as everything passed

Question 9

With critical region what are you doing

Answer 9

Essentially finding out the values thst if fall in will automatically lead to a rejectionl

Why use?
Because if yiu wwnt to test fir number if samples it becomes easy

Question 10

How to do TWO TAIL TEST Z
FIRST WHAT IS THE DIFFERENCE

Answer 10

A two tail test is testing for any sort of CHANGE WHATSOVER , good or bad

Thus the H1 is now that the probabiltiy is NO LONGER EQUAL TO WHAT EXPECTED

Here yiu have to test in bith tails , might not be enough evidence ti suggest they went up but enough ti suggest they went down etc

Question 11

How do you do critical region

Answer 11

Your significance value is in bith tails, so DIVIDE SIGNIFICANCE VALUE BY 2

Then find bith crtical regions that follow this

And then see if kbserved fall

Question 12

How to to do 2 tail for PORBAILOTY

Answer 12

here you still test in one tail, but assume that this is the same p value in the other tail

Thus at the end MULTIPLY P VALUE BY 2

then test and see

And reject accept

Question 13

And remember for critical region two tail and orobsbiltuhat you need to do to bith W

Answer 13

Alte erst IV enhootheidd different

Probability x 2 the p value

Critical divide significance by 2

Question 14

WHAT DOES A NON EMPTY TAIL FOR CRITICAL VALUE Mean

Answer 14

Essentially if 0 satisfies everything its empty

So for it to be non empty atleast 0 gotta not satisfy

And this makes easy too by doing ncr method just simple log

Remember tho log decimal = -, thus switch insauakity