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Hi i have seen few videos and read some articles as well but i am still confused, i'll trying quoting the example i saw. Helen sells chocolate nutties which claims to have 70gm or more peanuts in a 200 gm chocolate. Customers complains of chocolate not having enough peanuts.so

Null hypthesis : Chocolate contains >=70gm peanuts Alternate hypothesis : chocolate contains <70 gms peanuts

Helen selects significance level of 0.05%

Helen takes some samples and find out average amount of peanuts in chocolates it comes out to be 68.7 gms

Now she finds out the p-value for this statistical test, it comes out to be - 0.18 =18%

What is stated in video : since the p-value is high, which means there is higher chance (18%, which i higher than significance level) of occurence of what we have observed ( mean to be 68.7 gm), "if null hypothesis is true". So we can not reject the null hypthesis.

Confusion : P-value states if null hypothesis is true, then how likely is to get the results like we have got. If we consider chocolate contains >=70 gm of peanuts as true, and the chances of getting mean of 68.7 gm from the samples is high (18 %) then shouldn't we reject the null hypothesis because if chocolate are having >=70 gm of peanuts then getting chances less peanuts should be very low?? And had we got the p value as 0.01 (1%) the we should accept the null hyothesis as there is very less chance of getting less peanuts..

Help please...

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If we consider chocolate contains >=70 gm of peanuts as true, and the chances of getting mean of 68.7 gm from the samples is high (18 %) then shouldn't we reject the null hypothesis because if chocolate are having >=70 gm of peanuts then getting chances less peanuts should be very low?? And had we got the p value as 0.01 (1%) the we should accept the null hyothesis as there is very less chance of getting less peanuts.

I am not sure exactly what the source of your confusion is. Reading your last sentence, it seems that you think that the smaller the $p$-value, the less evidence there is that the null hypothesis is wrong. That's not correct. The smaller the $p$-value, the more evidence there is against the null hypothesis. Small $p$-values mean that there is a low probability of observing the sample mean (of 68.7) if the population mean was in fact equal to the value in the null hypothesis (70).

The way to think about $p$-value here is by using it to answer the question "could the sample mean of 68.7 have come from a population distribution with the mean of 70 (or higher)"? The higher the $p$-value, the more confident you can be that it could, and that the population does in fact have a mean of 70, which supports the null hypothesis. A small $p$-value would mean that the observed sample mean (68.7 in your case) is unlikely to come from a population distribution with the "true" mean of 70. In other words, it would indicate that 68.7 is significantly different from 70 to the point of this evidence suggesting that 70 is not the "true" population mean. So it would serve as evidence against the null hypothesis.

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  • $\begingroup$ Thanks Alex, your second para helped me to get the gist of it, i should think it as way to answer the question...It makes sense that way,, thanks again.. $\endgroup$ – user2889674 May 7 '19 at 17:40

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