Reflect on what you have just read. What you are going to learn to do by learning statistics is to learn the right way to make educated guesses. For most students, statistics is not a favorite course. It is viewed as hard, or cosmic, or just plain confusing. By now, you should be thinking: "I could just skip stat, and avoid making inferences about what populations are like by always collecting data on the whole population and knowing for sure what the population is like." Well, many things come back to money, and it is money that makes you take stat. Collecting data on a whole population is usually very expensive, and often almost impossible. If you can make a good, educated inference about a population from data collected from a small portion of that population, you will be able to save yourself, and your employer, a lot of time and money. You will also be able to make inferences about populations for which collecting data on the whole population is virtually impossible. Learning statistics now will allow you to save resources later and if the resources saved later are greater than the cost of learning statistics now, it will be worthwhile to learn statistics. It is my hope that the approach followed in this text will reduce the initial cost of learning statistics. If you have already had finance, you'll understand it this way—this approach to learning statistics will increase the net present value of investing in learning statistics by decreasing the initial cost.
Imagine how long it would take and how expensive it would be if Ann and Kevin decided that they had to find out what size sock every college volleyball player wore in order to see if volleyball players wore the same size socks as basketball players. By knowing how samples are related to populations, Ann and Kevin can quickly and inexpensively get a good idea of what size socks volleyball players wear, saving Foothill a lot of money and keeping John McGrath happy.
There are two basic types of inferences that can be made. The first is to estimate something about the population, usually its mean. The second is to see if the population has certain characteristics, for example you might want to infer if a population has a mean greater than 5.6. This second type of inference, hypothesis testing, is what we will concentrate on. If you understand hypothesis testing, estimation is easy. There are many applications, especially in more advanced statistics, in which the difference between estimation and hypothesis testing seems blurred.
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