statics PPMC Q

r=0.7628 and the calculated value from sampel size was 0.7155
As 0.7155<0.7628 is there insufficient evidence to reject H0 so insufficient evidence to prove correlation is postive?

How did you get those two numbers?

i got the r value from putting the table into the porudct moment function. And the other one from using sample size of 10 and 0.01% sig level in the formula booklet.

What is hypothesis test did you do, one tailed or two tailed?
It does help to see your working when posting a question.

my bad ill type it out
r was 0.7628
One tailed
Ho: p=0
H1: p>0
Value from formula booklet 0.7155<0.7628 therefore insufficient evidence to reject Ho and no evidence correlation coefficient is positive.

Ive not checked the values, but they look ok at a glance. However, is your final conclusion correct? If the data correlation was 1, 0.9, 0.8, 0.7, what would you conclude?

Im assuming 0.76 is from the data and 0.71 is the critical region from the hypothesis?

The crit region is the 0.76 so the 0.71 doesnt fall in it so you would dont reject it?

Before I check it, which number is the answer to part c)?

0.7628

But thats the oppoosite to what you said in the previous post.

The critical region boundary is ~0.71.
The pmcc value is ~0.76 so ...

im not sure what the names go by bc i only know it by r (product moment correlation) and the other as sample size value. I made it more confusing i apologise.
The pmcc is the 0.7628 and the other value is what you called the critical boundary is the 0.71

I agree with that (no need to apologise), so what do you conclude? If the pmcc was 1, what would you conclude? Similarly for 0.9, 0.8, 0.7 say.

I said that there was insufficient evidence to reject the Ho as it doesnt lie in the region.

Ill try for the last time, what would you conclude if the pmcc was 1? Is there sufficient evidence for a positive correlation?
Similarly for 0.9,0.8,0.7?

Oh yes bc the closer to 1 the more postive correlation it has.

So what do you conclude about this question?

that there is positive correlation?

Of course. Its really important to understand what the null hypothesis is and what the critical boundary/region corresponds to. The null hypothesis is that there is no (positive) correlation between the variables so pmcc<=0. This means that (weak) correlations < 0.71 (n=10) will not be strong enough to disprove this. For (strong) correlations > 0.71, there is enough evidence to support the fact that it is non-zero (posiitve). Obviously a correation =1 is the extreme case.

Note they've picked a 0.76 correlation here because a single tail test gives a p value 0.005, where as a two tail test gives a p-value > 0.01. So using the wrong test (one tail or two tail) will change the conclusion and hence get the question part right/wrong. They're deliberately using a pmcc just inside the critical region (close to the boundary) to get this.


https://www.statstutor.ac.uk/resources/uploaded/pearsons.pdf
Is decent and its good to get some pictures in your head about what typical data looks like. Just google
positive correlation null hypothesis
and get it straight.