 Hello and welcome to the session. In this session, we'll discuss how statistics can be used to make inferences about population parameters based on a random sample from that population. First of all, we'll understand the meaning of sample, population, statistics, parameters and inferences. Consider this example. A factory produces 5000 bulbs per day. The owner randomly selects 150 bulbs from these 5000 bulbs to check how many are defective. Now we see that all the 5000 bulbs produced in the factory form the population. These 150 bulbs randomly selected from the entire population represent the sample of the population. Statistic is the measure that describes the characteristic of a sample. Here the statistic is the number of defective bulbs in the sample of 150 bulbs. The statistic of a sample are used to draw conclusions about entire population and these are called statistical inferences. Here from the statistic of number of defective bulbs in the sample will help us to conclude or estimate the number of defective bulbs in the entire population. The value which is estimated from the sample will be the parameter. Thus we have the following definitions. First we have population and we define population as the entire collection of all the data of interest. It can be finite or infinite. Next we have sample which is defined as a subset of the population which is selected randomly from the population. Then we have statistic which is defined as a measurement describing the characteristic of the sample. It may vary from sample to sample. Next we have parameter which is defined as a measurement describing the characteristic of the population. It never varies and represents the entire population. And lastly we have statistical inference and statistical inference is when we draw conclusion about the population parameters using statistics of the sample. Let us consider an example. Astronomers typically determine the distance to a galaxy by measuring the distance to just a few stars within it and taking the mean of these distance measurements. Now we need to identify the population, sample, statistic and population parameter. As we know that the entire collection of all the data of interest constitute the population. So here population will be all stars in the galaxy. As sample is the subset of the population which is selected randomly from the population. So here stars selected for measurement will be the sample. Here statistics will be mean of the distance measurements. We know that statistic is a measurement describing the characteristic of the sample. It may vary from sample to sample. So here statistics will be equal to mean of distance between stars in sample and the earth. Next we shall find population parameter and we know that parameter is a measurement describing the characteristic of the population which never varies and represents the entire population. So here population parameter will be equal to mean of distance between all these stars and the earth. And now we are going to discuss types of parameters. There may be many types of parameters but we will discuss two types of parameters. First is population mean and second is population standard deviation. Population mean is denoted by mu and population standard deviation is denoted by sigma. Similarly we have sample statistics which is given by sample mean and is denoted by x bar and sample standard deviation is denoted by s. Thus we can say that sample mean helps in estimating population mean that is mu and sample standard deviation helps in estimating population standard deviation that is sigma. Let us now discuss how to draw inferences about population parameters. Here we discuss how to estimate population parameter in a single value. For example if we found that average number of defective bulbs in the sample of 150 bulbs is 14. Its sample mean that is x bar is equal to 14. So we can estimate the percentage of defective bulbs that is 14 upon 150 into 100 which is equal to 9.3% of the bulbs and we can say that 9.3% of the bulbs will be defective in the population and we should note that the estimate from the sample is not likely to be equal to the exact value for the population. So in this session we have learnt that how statistics can be used to make inferences about the population parameters based on a random sample from that population. This completes our session. Hope you enjoyed this session.