How do i determine the test statistic and the p value 60009

Name: how do i determine the test statistic and the p value 60009
Uploaded: 2022-06-22T12:26:29-08:00
Duration: 7 min 9 s
Channel: Jainendra Ojha
Description: how do i determine the test statistic and the p value 60009

Transcript

00:01 So let us first take a look at the introduction of the p value.

00:05 All right.

00:06 What is the p value? so the p value is basically in the context of the z test for the population mean new.

00:15 The p value is the measure of the strength of evidence, measure of strength of evidence against the null hypothesis.

00:37 Against the null hypothesis and the null hypothesis denoted by h0 that is provided by our sample data now basically the p value is the probability of getting the observed value of the test statistic or a value with a greater evidence against the null hypothesis so if our null hypothesis is going to be true the p value which is the probability it's called the conditional on the null hypothesis the this is now okay so this is our p value now let us look at to calculate what will be let us calculate look at the example of finding the p value okay so if you are going to look at to find the p value let us denote our null hypothesis which is h0 our null hypothesis is going to be such that the value of the mean me is going to be equals to mu not and our alternate hypothesis is such that the value of mu is greater than mu not so this is basically i'm going to take an example to elaborate what is the p value and the test statistics okay and here let us assume we have been given the normal distribution graph the distribution of z if h0 is true okay let me plot it distribution of z of z of z if h0 which is our null hypothesis is true so our graph will look like something it will be a normal distribution curve will build shaped so our graph is going to be like this and here this is our z value and this is our function of z all right so in the middle it is this value is basically zero then went up to infinity okay now this is negative for for this is 4 now mind this is just an example okay now suppose we wish to test the null hypothesis that the population mean which is denoted by mu is equal to mu not okay and let's suppose that we are sampling from a normally distributed population where the population standard deviation sigma is known okay so we have been given with the value of the sigma all right then our test statistic will be defined by this value the test statistics and sometimes it is also the z not okay sometimes it is z so the value z is going to be x bar minus mu over sigma over square root of n here sigma is the standard division n is the sample size okay so this is the z statistics x bar is the sample mean mu is the mean of the expectation and sigma the standard division of the mean and n is the number of elements in the lar sample which is basically the sample size so here the distribution of that test statistics if the null hypothesis is true is this normal distribution okay now suppose we go ahead and get a sample and we work out the value of z statistics and we find out that suppose we find out that the value the z statistics is 1 .53 so the value 1 .53 here is going to lie somewhere some somewhere here 1 .53 this is what the value going the value of 1 .5 3 is going to love now the large value of this test statistics are going to give the evidence against the null hypothesis in favor of this alternative okay and the p value which is the probability of getting the observed value of the test statis or something with the greater evidence against the null hypothesis and if the null hypothesis is true so values way out here in this right tail give evidence so this is our value in the right tail this value in the right tail give the evidence against the null hypothesis so the p value is going to be basically this probability this area is going to be our p value all right so the probability of getting what we observe here or something even further further out in this right tail so the p value is basically this shedding area which is in the blue color under the standard normal curve and we could also write out that the p value is the probability to the standard normal distribution variable taking on a value at least so the p value is basically the value of the x taking on a value as one observed in our sample to be greater than the value which is if z if z is if z is going to be 1 .53 then the probability that z is greater than 1 .53 the probability that z is going to be greater than 1 .53 is going to be our p value okay so our p value so our p value is basically going to be the probability that z is greater than 1 .53 and if you are going to use the standard normal distribution table or in case we can if you are going to use the calculator, then this value will come out to be 0 .063.

06:26 0 .063.

06:27 Therefore we can say that the p value is going to be 0 .063 and this is the formula to calculate the test statistics...

Question

How do I determine the test statistic and the p value?

Question

How do I determine the test statistic and the p value?

Please give Ace some feedback