 Hello and welcome to this session. In this session, we will use data from a randomized experiment to compare two treatments. Also, we will use simulations to decide if differences between parameters are significant. Now, let us discuss hypothesis testing. Now, suppose I have a coin and I want to know whether the coin is fair. To know this, I will perform an experiment of flipping a coin to know whether it is fair or not. Thus see, I have two equations, is coin fair, is coin unversions come under the domain of hypothesis. For this, I assume coin is fair. Then perform the experiment, then draw conclusion from the experiment to know whether my assumption about coin was true or not. Now, if the assumption is not true, then I draw conclusion that coin is not fair. So, I made a hypothesis that coin is fair. But after experiment, I reached the conclusion the coin is not fair. Another hypothesis assumed is called null hypothesis. But I rejected the null hypothesis and arrived at conclusion that coin is not fair. This is hypothesis. Now, null hypothesis is denoted by H0 and alternative hypothesis is denoted by H1. Now, these hypothesis are stated that they are mutually exclusive. That is, if one is true, then other must be false and vice versa. We either accept null hypothesis or reject null hypothesis. And if we reject null hypothesis, it means we are accepting alternative hypothesis. In tossing a coin, we stated null hypothesis H0 as coin is fair and alternative hypothesis H1 as coin is not fair. Experiment, we rejected H0 and we accepted. If we want to find whether there is a significant difference between means of two populations or not, let mu1 and mu2 be population means we define null hypothesis H0 as mu1 is equal to mu2. That is, there is no significant difference between means of two populations and alternative hypothesis H1 as mu1 is not equal to mu2. That is, there is no significant difference between means of two populations. They affect or reject the null hypothesis. Now, let us discuss null hypothesis about an experiment. Now, we know that there is an experiment with this control group. And other is, now suppose we measure a difference between the control and treatment groups on the treatment or if it is just a chance result of the choice of the groups. For this, we resend all the data. Now, let us understand using illustration, a randomness experiment test. Whether this randomness experiment affects the total yield in kilograms, the table below shows the results of the control and treatment groups compared with the differences resulting from chance. Now, to perform this experiment, we first need to find means of control and treatment groups. Now, instead of means, we will calculate mean of treatment group of the means or negative and it can be 0 when mean of consumption and mean of upon number of observations and this is 0.9 upon 10 is equal to sum of observations upon number of observations and this is equal to 13.7 upon 10 which is equal to 1.37. Each of the means is equal to mean of treatment group that is 1.69 minus mean of control group that is 1.37 and this is equal to 0. Now, in step 2, combine measurements and re-sample. Now, working in pairs to make 20 equal sized pieces and write one yield measurement on each and place the pieces in a bag then shake in 10 pieces in the bag consumer and then perform the resendment experiment by then in third step Steal the null hypothesis and alternate the hypothesis and for this activity, the null hypothesis H0 is given as has no effect on the yield of the cherry tomato plants on the yield of the cherry tomatoes evaluate the null hypothesis that the experiment is responsible for the difference in yield you need strong evidence to reject the null hypothesis to evaluate the null hypothesis, compare the experimental difference of means with the re-sampling differences Now, in step 3, minus mean of control group the differences in a histogram to re-samplings can be made using a graphing calculator In step 2 sampling data, we have sample difference of means at 0.32 or a vertical line on histogram to represent this difference of means lies in one of the tails of the re-sampling distribution then re-sampling gave a difference of means at least as large as the experimental difference hence for rejecting the null hypothesis more specifically, the difference of means falls outside of the middle 95% of the re-sampling differences of the means the null hypothesis, the 95% we have discussed about hypothesis testing and we have used simulations between parameters are significant or not and this completes our session hope you all have enjoyed the session