 Hello and welcome to the session. In this session we shall discuss making predictions and comparison of two samples. We choose a sample from the population when we want to know something or to draw some conclusion or to predict something. So we choose a sample from the population when we want to know something or to draw some conclusion or to predict something and then we survey the sample and draw the required result. As we have already discussed for valid results the sample should be chosen very carefully and now we can learn how to make predictions. Now let us take an example to understand predictions. There are 1170 students in our school. You ask 65 randomly chosen students what their hobby is and we get to know that 27 students like reading, 30 like travelling and 8 like stand collecting predict the number of students in the school who like travelling. If the prediction appropriate give reason. First we find the fraction of the students who have the hobby of travelling and we get this fraction by deciding the number of students who have the hobby of travelling by total number of students in the sample and we know that 30 students like travelling and there are 65 students in the sample. So we get this fraction as 30 by 65 which is equal to 6 upon 13. Now to find M we multiply this fraction by the total number of students in the school which is given by 15170 and we get 6 multiplied by 90 which is equal to 540. So we can say 540 students have the hobby of travelling. Now we need to take whether the prediction is appropriate or not. As we have already studied for this the three conditions of reasonable sample must be satisfied and the conditions are sample should be selected at random. It should be representative of the population and it should be large enough to provide accurate data and here in this example the sample is chosen randomly. It is also a representative of the population and it is large enough to provide accurate data. So we can say the prediction is appropriate. Now whatever conclusion we draw from sample about the population are valid only if the sample is representative of that population a person should consider all the aspects of the population and then choose a sample preferences should not be given While making the sample for this let us consider another example. In our school students are divided in four houses each house having the captain the principal wants to know which the most famous captain in the school is he surveys 50 students and draws his conclusion. Now in this sample the teacher should take into consideration that each house student has their representatives in the sample only then the sample will give valid conclusion. So here the teacher should take into consideration that each house student has their representatives in the sample only then the sample will have valid conclusion. Now we can learn comparison of two samples and then this we can compare the two samples to know which sample is good for making predictions where we again take an example which sample is better for making a prediction so did the number of defective births manufactured per day in a factory sample A a random sample of 400 births from 15 machines sample B a random sample of 400 births from one machine and now we shall see out of both these samples which sample is a better representative now consider sample A here the sample is random also it represents the population as it says a random sample of 400 births so we can say that the sample is random and it also represents the population it considers the product produced by 15 machines which is an appropriate thing because births have been produced by different machines also the size of the sample is large enough and the three conditions are satisfied now in sample B there is a random sample of 400 births from one machine so here we have seen only one machine is chosen and sample is chosen from only that machine that the births are being produced by several machines so we can say it is not an appropriate sample it does not represent the population thus we can say that sample A is a better sample to make predictions this concludes our session hope you enjoyed this session