Statistics Essentials For Dummies by Deborah Rumsey

hypothesis in this case would be as follows: H o : μ = 5.
What's the alternative?
Before actually conducting a hypothesis test, you have to put two possible hypotheses on the table — the null hypothesis is one of them. But, if the null hypothesis is found not to be true, what's your alternative going to be? Actually, three possibilities exist for the second (or alternative) hypothesis, denoted H a . Here they are, along with their shorthand notations in the context of the example:
The population parameter is not equal to the claimed value (H a : μ ≠ 5).
     
The population parameter is greater than the claimed value (H a : μ > 5).
     
The population parameter is less than the claimed value (H a : μ < 5).
     
Which alternative hypothesis you choose in setting up your hypothesis test depends on what you're interested in concluding, should you have enough evidence to refute the null hypothesis (the claim). For example, if you want to test whether or not a company is correct in claiming its pie takes 5 minutes to make, you use the not-equal-to alternative. Your hypotheses for that test would be H o : μ = 5 versus H a : μ ≠ 5.
If you only want to see whether the time turns out to be greater than what the company claims (that is, the company is falsely advertising its prep time), you use the greater-than alternative, and your two hypotheses are H o : μ = 5 versus H a : μ > 5. Suppose you work for the company marketing the pie, and you think the pie can be made in less than 5 minutes (and could be marketed by the company as such). The less-than alternative is the one you want, and your two hypotheses would be H o : μ = 5 versus H a : μ < 5.
Knowing which hypothesis is which
How do you know which hypothesis to put in H o and which one to put in H a ? Typically, the null hypothesis says that nothing new is happening; the previous result is the same now as it was before, or the groups have the same average (their difference is equal to zero). In general, you assume that people's claims are true until proven otherwise.
Hypothesis tests are similar to jury trials, in a sense. In a jury trial, H o is similar to the not-guilty verdict, and H a is the guilty verdict. You assume in a jury trial that the defendant isn't guilty unless the prosecution can show beyond a reasonable doubt that he or she is guilty. If the jury says the evidence is beyond a reasonable doubt, they reject H o , not guilty, in favor of H a , guilty.
In general, when hypothesis testing, you set up H o and H a so that you believe H o is true unless your evidence (your data and statistics) show you otherwise. And in that case, where you have sufficient evidence against H o , you reject H o in favor of H a . The burden of proof is on the researcher to show sufficient evidence against H o before it's rejected. (That's why H a is often called the research hypothesis , because H a is the hypothesis that the researcher is most interested in showing.) If H o is rejected in favor of H a , the researcher can say he or she has found a statistically significant result; that is, the results refute the previous claim, and something different or new is happening.
Finding sample statistics
After you select your sample, the appropriate number-crunching takes place. Your null hypothesis makes a statement about what the population parameter is (for example, the proportion of all women who have varicose veins or the average miles per gallon of a U.S.-built light truck). You need a measure of how much your results can be expected to change if you took a different sample. In statistical jargon, the data you collect measure that variable of interest, and the statistics that you calculate will include the sample statistic that most closely estimates the population parameter. If you're testing a claim about the proportion of women with varicose veins, you need to calculate the proportion of women in your sample who have varicose veins. If you're testing a claim about the average