## Press STAT and the right arrow twice to select TESTS.

*State what will happen if the experiment doesn’t make any difference.* That’s the null hypothesis–that nothing will happen. In this experiment, if nothing happens, then the recovery time will stay at 8.2 weeks.

The null hypothesis is a statement that you want to test. In general, the null hypothesis is that things are the same as each other, or the same as a theoretical expectation. For example, if you measure the size of the feet of male and female chickens, the null hypothesis could be that the average foot size in male chickens is the same as the average foot size in female chickens. If you count the number of male and female chickens born to a set of hens, the null hypothesis could be that the ratio of males to females is equal to a theoretical expectation of a 1:1 ratio.

## Tests for one measurement variable

It is known that the survival rate for individuals afflicted with a certain disease in a certain community is 90%. If 10 persons in the community contract the disease, what is the probability that (a) None will die (b) 50% will survive (c) at least 3 will die (d) exactly 3 will survive

## Where:Phat is calculated in Step 2P the (.05)Q is 1 – p

Usually, the null hypothesis is boring and the alternative hypothesis is interesting. For example, let's say you feed chocolate to a bunch of chickens, then look at the sex ratio in their offspring. If you get more females than males, it would be a tremendously exciting discovery: it would be a fundamental discovery about the mechanism of sex determination, female chickens are more valuable than male chickens in egg-laying breeds, and you'd be able to publish your result in *Science* or *Nature*. Lots of people have spent a lot of time and money trying to change the sex ratio in chickens, and if you're successful, you'll be rich and famous. But if the chocolate doesn't change the sex ratio, it would be an extremely boring result, and you'd have a hard time getting it published in the *Eastern Delaware Journal of Chickenology*. It's therefore tempting to look for patterns in your data that support the exciting alternative hypothesis. For example, you might look at 48 offspring of chocolate-fed chickens and see 31 females and only 17 males. This looks promising, but before you get all happy and start buying formal wear for the Nobel Prize ceremony, you need to ask "What's the probability of getting a deviation from the null expectation that large, just by chance, if the boring null hypothesis is really true?" Only when that probability is low can you reject the null hypothesis. The goal of statistical hypothesis testing is to estimate the probability of getting your observed results under the null hypothesis.

## The z-score is:.512 – .5 / √(.5(.5) / 4300)) = 1.57

In many statistical tests, you’ll want to either reject or support the . For elementary statistics students, the term can be a tricky term to grasp, partly because the name “null hypothesis” doesn’t make it clear about *what *the null hypothesis actually is!

## Look up Step 3 in the to get .9418.

The null hypothesis can be thought of as a *nullifiable *hypothesis. That means you can nullify it, or reject it. What happens if you reject the null hypothesis? It gets replaced with the which is what you think might actually be true about a situation. For example, let’s say you think that a certain drug might be responsible for a spate of recent heart attacks. The drug company thinks the drug is safe. The null hypothesis is always the accepted hypothesis; in this example, the drug is on the market, people are using it, and it’s generally accepted to be safe. Therefore, the null hypothesis is that the drug is safe. The alternate hypothesis — the one you want to replace the null hypothesis, is that the drug *isn’t* safe. Rejecting the null hypothesis in this case means that you will have to prove that the drug is not safe.