In everyday life,we often have to make decisions based on incomplete information. These may be decisions that are important to us such as, “Will I improve my biology grades if I spend more time studying vocabulary?” or “Should I become a chemistry major to increase my chances of getting into med school?” This section is about the use of hypothesis testing to help us with these decisions. Hypothesis testing is a kind of statistical inference that involves asking a question, collecting data, and then examining what the data tells us about how to procede. In a formal hypothesis test, hypotheses are always statements about the population. The hypothesis tests we will involve statements about the average values (means) of some variable in the population. For example, we may want to know if the average time that college freshmen spend studying each week is really 20 hours per week. We may want to compare this average time spent studying for freshmen that earned a CGPA of 8.0 or higher and those that did not.
Developing Null and Alternative Hypotheses
In statistical hypothesis testing, there are always two hypotheses. The hypothesis to be tested is called the null hypothesis and given the symbol H0. The null hypothesis states that there is no difference between a hypothesized population mean and a sample mean. It is the status quo hypothesis. For example,if we were to test the hypothesis that college fresh men study 20 hours per week,we would express our null hypothesis as:
H0 :µ = 20
We test the null hypothesis against an alternative hypothesis, which is given the symbol Ha. The alternative hypothesis is often the hypothesis that you believe yourself! It includes the outcomes not covered by the null hypothesis. In this example, our alternative hypothesis would express that fresh men do not study 20 hours per week:
Ha :µ not equals to 20
Deciding Whether to Reject the Null Hypothesis: One and Two-Tailed Hypothesis Tests
The alternative hypothesis can be supported only by rejecting the null hypothesis. To reject the null hypothesis means to ﬁnd a large enough difference between your sample mean and the hypothesized (null) mean that it raises real doubt that the true population mean is 20. If the difference between the hypothesized mean and the sample mean is very large, we reject the null hypothesis. If the difference is very small, we do not. In each hypothesis test, we have to decide in advance what the magnitude of that difference must be to allow us to reject the null hypothesis. Below is an overview of this process. Notice that if we fail to ﬁnd a large enough difference to reject, we fail to reject the null hypothesis. Those are your only two alternatives.