It may seem obvious, but a population is all of the members of a certain group. A sample is some of the members of the population. The same group of individuals may be a population in one context and a sample in another. The women in your stat class are the population of "women enrolled in this statistics class", and they are also a sample of "all students enrolled in this statistics class". It is important to be aware of what sample you are using to make an inference about what population.
How exact is statistics? Upon close inspection, you will find that statistics is not all that exact; sometimes I have told my classes that statistics is "knowing when its close enough to call it equal". When making estimations, you will find that you are almost never exactly right. If you make the estimations using the correct method however, you will seldom be far from wrong. The same idea goes for hypothesis testing. You can never be sure that you've made the correct judgement, but if you conduct the hypothesis test with the correct method, you can be sure that the chance you've made the wrong judgement is small.
A term that needs to be defined is probability. Probability is a measure of the chance that something will occur. In statistics, when an inference is made, it is made with some probability that it is wrong (or some confidence that it is right). Think about repeating some action, like using a certain procedure to infer the mean of a population, over and over and over. Inevitably, sometimes the procedure will give a faulty estimate, sometimes you will be wrong. The probability that the procedure gives the wrong answer is simply the proportion of the times that the estimate is wrong. The confidence is simply the proportion of times that the answer is right. The probability of something happening is expressed as the proportion of the time that it can be expected to happen. Proportions are written as decimal fractions, and so are probabilities. If the probability that Foothill Hosiery's best salesperson will make the sale is .75, three-quarters of the time the sale is made.
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