I do not understand how to test a hypothesis even though I can picture what they are talking about, it's so confussing, can you help?
You will have two hypotheses; the null hypothesis and the alternative hypothesis.
The null hypothesis generally means that the data of interest (mean of a population, etc...) is not different from the stated claim. The alternative is that there is a statistical difference.
The general procedure is to list the hypotheses. Then, using how certain you want to be (the significance level), you generate a test criterion. You then compare the sample data to the test criterion. The test criterion allows you to create a "cutoff point" -- it divides the region under the curve into regions. Beyond the cutoff point and it is unlikely that a random sample would produce this result so you reject the null hypothesis.
Basically what you are doing is finding the probability that a truly random sample could differ from the actual mean by some amount. If the probability is low, but the sample is far from the stated mean, then it is unlikely to have occurred by chance and the null hypothesis should be rejected.
The test criterion you generate depends on the data you are working with. The type of test depends on whether you are comparing means or variances or something else, on whether you know the population standard deviation, and on the size of the sample.
Perhaps an example would help:
The mean hourly wage is $9.50; we want to compare the local wage to the national average. A random sample of 75 people is polled with an average wage of `bar(x)` .
The null-hypothesis is `mu=9.5` . The alternative hypothesis is `mu <9.5` . (It could be `mu!=9.5` or `mu>9.5` depending on what you suspect is true.)
If we know the population standard deviation, s, we compute the test value : `z=(bar(x)-9.5)/(s/sqrt(75))` (You will be given s and `bar(x)` or you will be able to compute them.)
Suppose we want the 90% confidence level. Then `P(z<c)=.1` implies that c=-1.28. Thus the rejection region is z<-1.28
If the computed test value is less than -1.28 you reject the null hypothesis.