# Math Help - understanding the meaning of the answer

1. ## understanding the meaning of the answer

All the answers to these excercices on hypothesis testing go like this : " therefore reject H_0 at a alfa greater than **(number)** " WHat does it mean? For example, at this last excercice I got that the P-value was 0.0367 and alfa was 0.05 and H_1 was >. So P should have been > than alfa. But this was not the case, and I rejected. I go and see the answer and the book says "therefore reject H_0 at a alfa greater than 3.67%" What does it mean at a alfa greater then ..? And shall I always say that in my solution?

Thank you so much.

2. Originally Posted by 0123
All the answers to these excercices on hypothesis testing go like this : " therefore reject H_0 at a alfa greater than **(number)** " WHat does it mean? For example, at this last excercice I got that the P-value was 0.0367 and alfa was 0.05 and H_1 was >. So P should have been > than alfa. But this was not the case, and I rejected. I go and see the answer and the book says "therefore reject H_0 at a alfa greater than 3.67%" What does it mean at a alfa greater then ..? And shall I always say that in my solution?

Thank you so much.
Your probability is less than the significance level and therefore your result is significant. This means that you reject the null hypothesis in favour of the alternative hypothesis

3. Originally Posted by Glaysher
Your probability is less than the significance level and therefore your result is significant. This means that you reject the null hypothesis in favour of the alternative hypothesis
So you mean, I have a probability 3.67% that H_0 is true, but we said "No! We want the treshold to be 5%! Less than 5% we do not accept anything!" But you say "but the true probability to get H_0 true is 3.67 % from the p-value" "3.67%? Too low!Reject H_0!"

Is this it? I know the way I say it is really inappropriate (and embarassing), but I do it when I really have hard hard time understanding..

4. Originally Posted by 0123
So you mean, I have a probability 3.67% that H_0 is true, but we said "No! We want the treshold to be 5%! Less than 5% we do not accept anything!" But you say "but the true probability to get H_0 true is 3.67 % from the p-value" "3.67%? Too low!Reject H_0!"

Is this it? I know the way I say it is really inappropriate (and embarassing), but I do it when I really have hard hard time understanding..

No, more like 3.67% chance of getting the observed value given that $H_0$ is true. Because this is less than 5% we judge it to be too unlikely to have happened and reject $H_0$ in favour of $H_1$

5. Originally Posted by Glaysher
No, more like 3.67% chance of getting the observed value given that $H_0$ is true. Because this is less than 5% we judge it to be too unlikely to have happened and reject $H_0$ in favour of $H_1$
Sorry, I am afraid I do not understand. You mean, our computation revealed that , given $H_0$ true, we get that value about 3.67% of the times. But If $H_0$ was true we expected the value to happen at least 5% of times. SO we infer that $H_0$ cannot be true. Is this it? Thank you.

6. Originally Posted by 0123
Sorry, I am afraid I do not understand. You mean, our computation revealed that , given $H_0$ true, we get that value about 3.67% of the times. But If $H_0$ was true we expected the value to happen at least 5% of times. SO we infer that $H_0$ cannot be true. Is this it? Thank you.
If you give me an example to go through it will be easier to explain as hypothesis testing can be used in a variety of circumstances

One example could be:

Pepsi claim their coke is better than Coca Cola. Fifteen out of twenty people who participated in a taste test claimed Pepsi was better. Perform a hypothesis test at the 5% level to test this claim

Assuming that the people's choices were 50/50 this can be modelled by:

$X~B(20,0.5)$

Giving hypotheses:

$H_0 = 0.5$
ie there is no difference between Pepsi and Coca Cola

$H_1 > 0.5$
ie Pepsi is better

We assume $H_0$ to be true

We calculate the probability of getting the observed value or more as we check the ends of the distribution (the probability of getting the exact observed value being small anyway)

P(X > 15) = 1 - P(X < 14) = 1 - 0.9793 = 0.0207

We compare this probability with our 5%

0.0207 < 0.05

Since the probability is less than 5% we judge it to be unlikely to have happened given our initial assumption. Therefore the initial assumption is wrong. Therefore reject $H_0$ in favour of $H_1$. The evidence suggests Pepsi's claim is true