# C3\_W4(p-value) : Why are we rejecting null hypothesis when type-1 error is under significance level? (https://www.coursera.org/learn/machine-learning-probability-and-statistics/lecture/znGVX/p-value)

**URL:** <https://community.deeplearning.ai/t/c3-w4-p-value-why-are-we-rejecting-null-hypothesis-when-type-1-error-is-under-significance-level-https-www-coursera-org-learn-machine-learning-probability-and-statistics-lecture-zngvx-p-value/702758>\
**Category:** Probability & Statistics for Machine Learning &...\
**Tags:** week-module-4\
**Created:** [October 3, 2024, 4:42pm UTC](https://community.deeplearning.ai/t/c3-w4-p-value-why-are-we-rejecting-null-hypothesis-when-type-1-error-is-under-significance-level-https-www-coursera-org-learn-machine-learning-probability-and-statistics-lecture-zngvx-p-value/702758 "2024-10-03T16:42:38Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![GORRELA\_SRI\_SATYA\_VE](https://avatars.discourse-cdn.com/v4/letter/g/a9a28c/32.png) [@GORRELA\_SRI\_SATYA\_VE](https://community.deeplearning.ai/u/GORRELA_SRI_SATYA_VE)\
**Post date:** [October 3, 2024, 4:42pm UTC](https://community.deeplearning.ai/t/c3-w4-p-value-why-are-we-rejecting-null-hypothesis-when-type-1-error-is-under-significance-level-https-www-coursera-org-learn-machine-learning-probability-and-statistics-lecture-zngvx-p-value/702758/1 "2024-10-03T16:42:39Z")

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![Screenshot 2024-10-03 at 21.57.15](https://global.discourse-cdn.com/dlai/original/3X/d/d/dd38c74f94201887a38996a166ab684b4657bb67.jpeg)

here if you see null hypothesis is mean = 66.7 and alternative hypothesis is mean \> 66.7

if probability of sample mean \> 68.442 increases then we should reject null hypothesis right? If it is under significance level then why are we rejecting null hypothesis ? (I’m bit confused about this topic)

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**Author:** ![Deepti\_Prasad](https://sea1.discourse-cdn.com/dlai/user_avatar/community.deeplearning.ai/deepti_prasad/32/165831_2.png) [@Deepti\_Prasad](https://community.deeplearning.ai/u/Deepti_Prasad)\
**Post date:** [October 3, 2024, 5:12pm UTC](https://community.deeplearning.ai/t/c3-w4-p-value-why-are-we-rejecting-null-hypothesis-when-type-1-error-is-under-significance-level-https-www-coursera-org-learn-machine-learning-probability-and-statistics-lecture-zngvx-p-value/702758/2 "2024-10-03T17:12:51Z")

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hi @GORRELA_SRI_SATYA_VE

Image is trying to explain type 1 error probability where we reject the null hypothesis based on the std mean calculation and p value being either equal to or less than 0.05 for the designated std mean where as it shouldn’t

We are not suppose to reject null hypothesis here as the std mean is greater for 5% than the std mean at 50%

Image is only explaining type 1 error probability

 ![2022_10_MicrosoftTeams-image-209](https://global.discourse-cdn.com/dlai/original/3X/2/d/2d38e9992cad4141fd67e59ef00b94639c460820.jpeg)

Regards  
DP

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**Author:** ![rmwkwok](https://sea1.discourse-cdn.com/dlai/user_avatar/community.deeplearning.ai/rmwkwok/32/126977_2.png) [@rmwkwok](https://community.deeplearning.ai/u/rmwkwok)\
**Post date:** [October 5, 2024, 12:36am UTC](https://community.deeplearning.ai/t/c3-w4-p-value-why-are-we-rejecting-null-hypothesis-when-type-1-error-is-under-significance-level-https-www-coursera-org-learn-machine-learning-probability-and-statistics-lecture-zngvx-p-value/702758/3 "2024-10-05T00:36:03Z")

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Hello, @GORRELA_SRI_SATYA_VE,

The larger the sample mean \bar{X}, the more right (extreme) it is to the population mean \mu, the more likely the sample does not belong to the population (H\_0) and thus H\_0 rejected. In other words, very “right” (“extreme”) sample is unlikely generated by the population (or generated under H\_0)!

But how right is right enough? We use \alpha for that!

 ![image](https://global.discourse-cdn.com/dlai/original/3X/f/b/fb4b1ea10c02f96b552ba878d283712322dcee8f.png)

\alpha is the area (at the right tail) in which any sample fallen is considered "unlikely by the population (or unlikely under H\_0). \alpha is a criteria and since 68.442 falls within it, we reject H\_0!

> [@GORRELA\_SRI\_SATYA\_VE](#):
>
> If it is under significance level then why are we rejecting null hypothesis ?

Because the more the p-value is smaller than the significance level (\alpha), the more unlikely it is genereted under H\_0, so we reject it!

Remember, small p-value means more extreme .

> [@GORRELA\_SRI\_SATYA\_VE](#):
>
> if probability of sample mean \> 68.442 increases then we should reject null hypothesis right?

I suppose “probability of sample mean \> 68.442” means the p-value, right? In that case, we reject H\_0 if the p-value is less than \alpha, so it is not “increase” because if it increases to a level that is larger than \alpha, we will not reject H\_0.

Cheers,  
Raymond

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**Author:** ![GORRELA\_SRI\_SATYA\_VE](https://avatars.discourse-cdn.com/v4/letter/g/a9a28c/32.png) [@GORRELA\_SRI\_SATYA\_VE](https://community.deeplearning.ai/u/GORRELA_SRI_SATYA_VE)\
**Post date:** [October 6, 2024, 7:00pm UTC](https://community.deeplearning.ai/t/c3-w4-p-value-why-are-we-rejecting-null-hypothesis-when-type-1-error-is-under-significance-level-https-www-coursera-org-learn-machine-learning-probability-and-statistics-lecture-zngvx-p-value/702758/4 "2024-10-06T19:00:42Z")

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thanks this makes sense. It clarified my confusion

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**Author:** ![rmwkwok](https://sea1.discourse-cdn.com/dlai/user_avatar/community.deeplearning.ai/rmwkwok/32/126977_2.png) [@rmwkwok](https://community.deeplearning.ai/u/rmwkwok)\
**Post date:** [October 12, 2024, 2:48am UTC](https://community.deeplearning.ai/t/c3-w4-p-value-why-are-we-rejecting-null-hypothesis-when-type-1-error-is-under-significance-level-https-www-coursera-org-learn-machine-learning-probability-and-statistics-lecture-zngvx-p-value/702758/5 "2024-10-12T02:48:28Z")

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You are welcome, @GORRELA_SRI_SATYA_VE!

Cheers!