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)

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

Regards

DP

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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!

\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!

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 .

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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thanks this makes sense. It clarified my confusion

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You are welcome, @GORRELA_SRI_SATYA_VE!

Cheers!