![]() You will now learn the answers to some important questions: What is margin of error, what are the method of calculating margins of error, how do you find the critical value, and how to decide on t-score vs z-scores. Now, when you use this sample mean to infer about the population mean, you won’t be able to get the exact population means. Hence, you take out a sample of, say, 100 students and find out the average scores of those 100 students. It may be time-consuming for you to study the entire population, i.e. Suppose you want to study the scores obtained in an examination by students in your college. A larger sample is likely to be a closer representative of the population than a smaller one. Common sense would say that if you increase the sample size, the chances of error will be less because you are taking a greater proportion of the population. The degree of accuracy depends on the sample taken – how the sample was selected, what the sample size is, and other concerns. Since the inferences are made about the population by studying the sample taken, the results cannot be entirely accurate. ![]() ![]() You then carry out some analysis using the sample and make inferences about the population. The best you can do is to take a random sample from the population – a sample that is a ‘true’ representative of it. This is because it is extremely costly, difficult and time-consuming to study the entire population. While you are learning statistics, you will often have to focus on a sample rather than the entire population.
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