# Math Help - Hypothesis testing

1. ## Hypothesis testing

http://www.xtremepapers.com/Edexcel/...%202006-01.pdf

Look at question 7 on the last page

so I know that for (ai)
H0: p = 0.2
H1: p <> 0.2 (does not equal)

Now when I carry out the test, if it was p>0.2 I would say
P(X>=9).... and then work out the answer
equall if it was p<0.2 I would say P(X<=9)

But given that it is p <>0.2 how do I carry out the test. Please can you explain as well!

For (b) I am again faced with the same issue
The distribution is
X-N(20,16)
H1 again is p<>0.2

so for my normal approx to I use
P(x>=18) or p(x<=18)

I will continuty correct once I understand the principle

thanks for the help!

2. ## Re: Hypothesis testing

This site is blocked by my company because it is classified as:

"Scam/Questionable/Illegal"

CB

4. ## Re: Hypothesis testing

Originally Posted by jsmith613

The null hypothesis $H_0$ is that $p=0.2$, and the alternative is that $p \ne 0.2$.

We reject the null hypothesis if the probability of the observed result or more extreme conditioned on the null-hypothesis being true is "small".

That is if:

$P(9{\text{ or more from }}20|H_0)<0.05$

Now since under the null hypothesis the distribution of the number of Deano readers in a sample of size $20$ has a binomial distribution $B(20,0.2)$ we can work out the probability on the left (and it is $\sim 0.01$), which is less than $0.05$ so we reject the null hypothesis.

However exact binomial calculations of the size required by this problem are beyond what is reasonable to expect in an exam, so you will either have to use an approximation or tables of critical values provided for this purpose.

You will note that the alternative hypothesis does not figure in this test.

Part (b) works in essentially the same manner except the sample size is now 100, and large(ish) sample approximations are probably appropriate.

CB

5. ## Re: Hypothesis testing

well what I was asking was how do I decide if I should use P(X<=9) or P(X>=9)

Is it becasue the E(X) - mean - is 4.
9 is above the mean so I calcuate P(X>=9) NOT P(X<=9)

for normal, mean is 20, value is 18 SO here is say P(X<=18) NOT P(X>=18)

thanks

6. ## Re: Hypothesis testing

Originally Posted by jsmith613
well what I was asking was how do I decide if I should use P(X<=9) or P(X>=9)

Is it becasue the E(X) - mean - is 4.
9 is above the mean so I calcuate P(X>=9) NOT P(X<=9)

for normal, mean is 20, value is 18 SO here is say P(X<=18) NOT P(X>=18)

thanks
You always ask what is the probability of observing a result this far or further from what is expected.

CB