Hypothesis testing often refers to two types of hypotheses: the null and alternative hypotheses. The null hypothesis is the statement that will be tested. The alternative hypothesis is the backup outcome that only plays a part in the test if testing the null hypothesis leads to a rejection of the hypothesis. For the purposes of testing a hypothesis three different ways, disregard the alternative hypothesis and focus only on the null.
A confidence interval is one hypothesis testing method, and is based on an estimation of the hypothesis's parameters. In a confidence interval test, the formula involves finding the mean of the sample and comparing it to the standard error to determine which is greater. Or, if you already know the sample mean's standard deviation, you can replace it with the standard error and approximate the confidence level for accepting the null hypothesis. In other words, this approximates how sure -- or confident -- one is with the hypothesis. The estimated confidence level, such as 95 percent, must be determined at the start of the test in order to assess how accurate the hypothesis is.
A one-tailed test is a test that measures the standard normal distribution, based on the hypothesis or assumption that the parameters being measured will be greater or less than a particular statistic. In a one-tailed test, the variables being tested are divided into two regions: a rejection region and an acceptance region. This is where the greater than or less than concepts come into play, as it dictates where the sample is divided into regions. The test is determined by the greater or less than value as stated in the hypothesis, and the hypothesis is rejected if data in the rejection region turn out to be true.
A two-tailed hypothesis test is one in which the null hypothesis states that the variables are equal to or not equal to something, such as a percentage estimate. In this type of test there are three regions to consider: two rejection regions and one acceptance region. In a two-tailed test, you will be able to determine whether or not to reject the null hypothesis based on evidence from either tail. In a two-tailed test, the acceptance region is smaller -- meaning it is more difficult to prove -- because of the two tails, or variables, within the test.