Hypothesis Testing

Question 1

How to do a test
Not critical

What remember

Answer 1

1) set p as probability and x number of
2) find null and alternative hypotheses
3) set your significance level (5% usually)
- determine what your test is , testing how likely it I’d to get this many things OR A MORE EXTREME VALUE Inna trial of this etc.
4) conduct test : if H0 is true then it will follow a binomial distribution
5) compare probability with signficance value : think that if your calculated probability is more than 5%, then there is a high chance it happens, so it is fair = do not reject null hypothesis. But if it is lower, low chance probably biased = reject

Question 2

What to remember for hypothesis testing if they give you 5 out of 10, what value you test for (is it 5?)

Answer 2

You need to test for the extremes, so go x is more than = to 5, so you can test all of that

Always remember to test for EXTREMES

Question 3

What to always remember for picking p(x= something)

Answer 3

Go for the most surprising result

- if resign for 6, go less

Question 4

In conclusion what should you say / never say

Answer 4

1) reject or accept null hypothesis based in significance level
2) say there is enough / not enough evidence to suggest

NEVER SAY THIS SHOWS, only considering evidence not proving anything

Question 5

What is the error with the testing and what would a company need to do to actually show they are correct

What is the error with setting significance levels

Answer 5

Even though they may have hit what they think, the sample size may be too low and so this is likely just due to chance

They will have to increase sample size to prove

2) the significance level is too high = then your results may lead you to not reject H0 when you should - probability of getting this is = to signficiance level, so a lower one better but more strict

Question 6

What’s going on when you are testing by finding critical region, what is this etc

Answer 6

This is just working back , instead of finding if your chosen value or above / below is less than 0.05 , your finding the range of values that would automatically be less than 0.05 = the CRITICAL REGION

If your chosen value then falls in this region, then automatically it gives you less than 0.05, so you reject H0 as is enough evidence to suggest it is wrong (not just by chance)

But if chosen value falls outside critical region, it would give you a value above 0.05, so there is not enough evidence to suggest the H0 is wrong

Conc
- you thus need to find out the smaller value for which a range would give you a probability less than 0.05…

Question 7

What are two tailed and one tailed tests

Answer 7

One tail test is where the direction of the change is specified

When dealing without knowning this, this = two tailed, you need to test for probabilities in BOTH DIRECTIONS !

Question 8

How to do two tailed for critical region

TWO KEY DIFFERENCES

Answer 8

Do everything same, except alternative hypothesis is that it’s not = to that

• THE FACT THAT IT IS TWO TAILED MEANS SIGNIFICANCE VALUE DIVIDES BY TWO, 2.5% IN EACH TAIL

Then find a critical region at both sides, more than and less than that probability .

Now If your value not in, then same rule do not reject

Question 9

How to do two tail for normal testing

Answer 9

Same thing, h1 is not equal to,

• now test for one extreme, but bare in mind that it’s two tailed , and this value is 2.5%
• as a result p value would be this multiplied by 2
• now compare this to 5%

And conclude

Question 10

Remember for calculating probabilities at the start for H0

Answer 10

Testing thst there is an even chance