Null Hypothesis (H0)
In many cases the purpose of research is to answer a question or test a prediction, generally stated in the form of hypotheses (is, singular form)  testable propositions. Examples:
Question Hypothesis Does a training program in driver safety result in a decline in accident rate? People who take a driver safety course will have a lower accident rate than those who do not take the course. Who is better in math, men or women? Men are better at math than women. What is the relationship between age and cell phone use? Cell phone use is higher for younger adults than for older adults. Is there a relationship between education and income? Income increases with years of education. Can public education reduce the occurrence of AIDS? The number of AIDS cases is inversely related to the amount of public education about the disease.
The statistical procedure for testing a hypothesis requires some understanding of the null hypothesis. Think of the outcome (dependent variable). From a statistical (and sampling) perspective), the null hypothesis asserts that the samples being compared or contrasted are drawn from the same population with regard to the outcome variable. This means that
The symbol H0 is the abbreviation for the null hypothesis, the small zero stands for null.
Oddly enough, we are in a sense betting against our research judgment. If we didn't think that some factor made a difference, we probably would not be doing the research in the first place. But statistically speaking, we temporarily adopt the critical stance that our independent variable does NOT matter.
Generally, when comparing or contrasting groups (samples), the null hypothesis is that the difference between means (averages) = 0. For categorical data shown on a contingency table, the null hypothesis is that any differences between the observed frequencies (counts in categories) and expected frequencies are due to chance.
Research Hypothesis (H1)
The research hypothesis (or hypotheses  there may be more than one) is our working hypothesis  our prediction, or what we expect to happen. It is also called the alternative hypothesis  because it is an alternative to the null hypothesis. Technically, the claim of the research hypothesis is that with respect to the outcome variable, our samples are from different populations (remember that population refers to the group from which the sample is drawn). If we predict that math tutoring results in better performance, than we are predicting that after the treatment (tutoring), the treated sample truly is different from the untreated one (and therefore, from a different population).
The research or alternative hypothesis is abbreviated as H1, and if there are more hypotheses, H2, H3, H4, etc.
Why the Null Hypothesis (H0)?
When we pose a research question, we want to know whether the outcome is due to the treatment (independent variable) or due to chance (in which case our treatment is probably not effective). For example, the claim that tutoring improves math performance generally does not predict exactly how much improvement. Each level of improvement has a different probability associated with it, and it would take a long time and a great deal of effort to specify the probability of each of the possible outcomes that would support our research hypothesis.
extraneous factors 
factors (variables) in addition to the independent variable, that might
be affecting the dependent variable (outcome). 
On the other hand, the null hypothesis is straightforward  what is the probability that our treated and untreated samples are from the same population (that the treatment or predictor has no effect)? There is only one set of statistical probabilities  calculation of chance effects. Instead of directly testing H1, we test H0. If we can reject H0, (and extraneous factors are under control), we can accept H1. To put it another way, the fate of the research hypothesis depends upon what happens to H0.



NOTE: The null hypothesis is NOT the opposite of the research hypothesis. The null hypothesis states that any effects observed after treatment (or associated with a predictor variable) are due to chance alone. Statistically, the question that is being answered is "If these samples came from the same population with regard to the outcome, how likely is the obtained result?"
Next section: Introduction to Inferential statistics (testing hypotheses)