H2 Maths

Teobkg SG

GCE A Level Maths Nov 97/Paper 2/ Qn 10

......The horticulturist wishes to test the hypothesis that the mean crop weight per plant is 5 kg, against the alternative hypothesis that the mean crop weight per plant is less than 5 kg. Carry out the test at 10% level of significance.

Ans: I carried out the Z-test. p-value =10.8 Therefore, do not reject the null hypothesis.

Next part of Qn............

Find the largest level of significance at which the test would result in rejection of the null hypothesis.

Ans: ??? I do not understand the qn. I would say that the lowest (but not the largest) level of significance to reject the null hypothesis is the p-value.

Could there be a misprint in the question. Can somebody provide som explanations?

Lee012lee SG

Critical P value is usually assumed to be at 5% level of significance but this question wants to make the calculated P value as the critical P value and so the question requires the siginficance level to get this critical p value.

Teobkg SG

Yes, the level of significance has to be at least 10.8 so that the null hypothesis can be rejected. Therefore, the question should ask for the smallest and not the largest level of significance.

wee_ws SG

Hi,

10.8% is the greatest lower bound.

Thanks!

Cheers,
Wen Shih

wee_ws SG

Hi,

This explanation may be clearer: 10.8% gives the largest possible rejection region of which the p-value lies within it. Note that the level of significance defines the rejection region.

Thanks!

Cheers,

Wen Shih

Teobkg SG

In a test of statistical hypotheses, the

P-value tells us the smallest level of significance at which the null hypothesis can be rejected.

Would you agree with the above definition of P-value?

Anonfire SG

for you to reject null hypothesis, p value must be less than 10.8 right?

im nto sure how to explain to you from here bout just consider this methods:

- use inverse norm (look at you Z-test formula and you will know how to do it)

- draw the hypothesis curve. you will understand better.

yup. i hope you get the answer. if you still dont know just look for your maths tutor.

wee_ws SG

Hi,

Let me try again to explain. It's a good habit to ask until the reason becomes clear and convincing.

At 10% significance level, p-value = 0.108 > 0.10 so we do not reject the null hypothesis. In order to reject the null hypothesis, there is a need to increase the significance level. If we increase it to 10.8%, the p-value matches exactly to it, so that we can reject the null hypothesis. Thus, 10.8% becomes the critical value for the level of significance.

Now, another way to look at the level of significance is this:a 10.8% level of significance refers to a probability of 0.108 of rejecting the null hypothesis when it is, in fact, true. We call this a Type I error and we want to minimise this error as far as possible.

When we increase the level of significance from 10% to 10.8% in order to reject the null hypothesis, we also increase this Type I error at the same time. With the need to minimise this error, we set a cap. Thus, the maximum that we should increase to is the value of 10.8%.

I hope this is much clearer and more comprehensive than all other explanations I have given thus far. Thanks for being inquisitive, because that gave me the opportunity to go deeper than usual :)

Thanks!

Cheers,
Wen Shih

wee_ws SG

Hi,

To add, p-value was not taught to students in 1997, or rather before H2 maths was implemented in 2006. The concept of alpha or Type I error was familiar to students then.

You are right to say that the p-value is the smallest level of significance at which the null hypothesis can be rejected. At the same time, this value happens to be the critical value to be used for the level of significance (to allow the p-value to lie within) and it is the largest possible Type I error that the statistician would want to commit when doing this hypothesis testing.

Thanks!

Cheers,
Wen Shih

jiaxing2 SG

hi,

wanted to ask about this p-value thing...

In the past, if i remember correctly, students were taught to use to value of test statistic, that is the z-value or t-value, to decide upon whether or not to reject hypothesis.

so are students now taught how to compute the P-value, or are they taught to just quote this value from the GC?

Is it redundant to teach about z-value and t-value now?...

jiaxing

wee_ws SG

Hi,

Students are taught to compute p-value using the GC. They are also taught how to compute z-value and t-value in case there are missing variables. You may wish to refer to my website on some 'hypothesis testing' questions where it is necessary to use test statistic to determine inequalities:

http://www.freewebs.com/weews/hypothesistesting.htm

Thanks!

Cheers,
Wen Shih