1. ## Hypothesis testing

The controller of examination of certain university claimed that at least 60% of the students have passed in the university.An examination is conducted to a random sample of 200 students and it is found that 140 students were passed in the examination.Test whether the controller is valid or not at 5% level of significance.

2. $\displaystyle H_0=.6$ vs. $\displaystyle H_a>.6$.

You can also use $\displaystyle H_0\le .6$.

You approximate via the CLT with a normal, most people ignore the $\displaystyle \pm .5$ here.

The rejection region is $\displaystyle (1.645,\infty)$ and the test stat is

$\displaystyle {\hat P-P_0\over \sqrt{{P_0Q_0\over n}}}={.7-.6\over \sqrt{{(.6)(.4)\over 200}}}$ (I only used capitals so you could read this.)

3. If the null hypothesis is p=0.6
What should be the alternative hypothesis?

4. Originally Posted by roshanhero
If the null hypothesis is p=0.6
What should be the alternative hypothesis?
I typed it right above, p>.6 in either case.
This is what you want to prove.

5. But, for the controller to be proved invalid,can't we use in alternative hypothesis,p<0.6

6. I am trying to prove this claim...
controller of examination of certain university claimed that at least 60%

AND the statement....the controller is valid.... ISN'T clear at all
It should say... the controller CLAIM is valid ....

IN any case if you want to 'prove' that p<.6, well a sample estimate $\displaystyle \hat p=.7$ certainly won't have you concluding that p is less than .6

7. Will it be a one tail test or a two tail test.

8. I already gave you my opinion.