 तो भी परिज़़ी आपना उपने नापाकता, तो बी अम्एखो तेसक थाद्गाँ बीशिस्गीग थाद्गीडेगोि से लिए खॉद concludाए थे लिए कि आपने खोग भी ढ़़ी परिज़ीडेगोग देखेगोग से नहीं, डरदाग लग आपनोयों फिरा के सकति आपने � exceptance region for the null hypothesis and we say that we keep 0.05% probability to reject it i.e. this is called rejection region which is on the tails and is in the middle of acceptance region what we do is we calculate probability and we are 95% sure that this null hypothesis is our true acceptance for null hypothesis and if our value comes in this tail then we say that we cannot accept our null hypothesis in fact our research hypothesis is that is true rather than the null hypothesis let's do an example a coin is tossed 20 times so n is 20 landing on head more than 6 times 20 times a coin is tossed and it landed on head more than 6 times so perform a hypothesis test at alpha 0.05% significance level to see if the coin is biased you have given the data you have tossed a coin and 6 times your head now you have to make your hypothesis, null hypothesis is always our hypothesis of no difference let's start the research with the null hypothesis where we give a neutral statement that there is no difference between x1 and x2 or coin is not biased, coin is fair or whatever so it's a neutral statement, a null hypothesis and again we make our research hypothesis which we say that coin is biased in favor of tails because you have said that there are more tails to test this hypothesis, similarly we make our research hypothesis null hypothesis or alternative hypothesis and to test this hypothesis we apply any statistical test it can be z test or t test or we are testing the binomial distribution so your question is that if the coin is fair it means that your value will come in this area that is your probability value p value which you calculate should be less than 0.05 if our probability value is less than 0.05 then our null hypothesis will be rejected null hypothesis will be rejected and if our probability calculated value falls in this area so this means that our null hypothesis is correct we will fail to reject the null hypothesis so let's calculate the probability and see where it is lying so again information is given that you have given the coin as 20n and you have given p and q how much will be p of course if you are tossing the coin as 1 by 2 and q will also be 1 by 2 n is 20 p is 1 by 2 and q is 1 by 2 first of all you have to calculate mean mean is equal to np which is equal to 20 multiplied by 1 by 2 which is equal to 10 after this you have to calculate standard deviation which is equal to npq under root which is equal to 20 multiplied by 1 by 2 multiplied by 1 by 2 under root which is equal to you can calculate it as 2.24 now you have the mean and standard deviation we should have the value of x to calculate z what it has said is landing on head more than 6 times so more than 6 means that again I have to draw a distribution here or more than 6 till you have not calculated mean you cannot draw an area in it first you have to calculate mean which is equal to 10 so more than 6 means that 6 will land on this side and more than 6 means that we have to find out all these areas for this 6 I have to find out the value of z so how will I find out the value of z for this 6 so I will say 6.5 will continue this because it is your x so I have told you to continue this we will write mean divided by standard deviation which we have drawn 2.24 plug in the values solve it z value of 1.56 next what we will do area find out you will look up in the table 1.56 corresponding area see how much it is we have found out the area so the area which we have drawn that is I have double checked in the table which is equal to this area is 0.4406 now what we have to see we have to do testing hypothesis and we have said that if these tails have p value probability this means that our null hypothesis will reject but if our value comes in between this means that our null hypothesis will be accepted instead of looking at the value of z we can find out tail value this tail value we can find out instead of this so if we want to find out the value of this tail this is 0.5 by the way we can do it by plus but already column C it has given the value of your tail which is equal to 0.0594 this is the tail value you can also get the tail value which is equal to 0.5 or 0.4406 which is equal to 0.9406 and subtract it from 1 so your value will come so if I subtract 0.9406 from 1 then this value will come 0.0594 I will write it clearly so that you can understand so it is 0.0594 which is this so what we have to calculate if we say that p value if it is smaller than 0.05 then null hypothesis will be rejected this is what we have written but what is our p value our p value is p is equal to 0.0594 this one so it is not smaller rather p is greater than 0.05 if this is the case that your calculated probability value is greater than 0.05 then you will fail to reject the null hypothesis so the conclusion we will take in hypothesis testing that our null hypothesis we are not rejecting it and we will say that the coin is not biased the coin is fair but if this p value is smaller then we will definitely say that the coin is biased so similarly in the binomial distribution there are many more in our everyday life in our social issues when you will conduct a research when you think that your outcome variable is categorical there are only two possible outcomes and you can make it yourself you can make any continuous variable to be binomial by bringing that variable into two categories only if you have a running score on anxiety if you have a score on the stats then you can pass if you have another experiment then you can bring it into two categories and find out its mean and standard deviation not only you can estimate the population parameter you can also find out the probability and you can also do the testing hypothesis that you can do any hypothesis through binomial test and if our calculated value p value of 0.05 will be smaller then we will reject our null hypothesis