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**Solution.** Because the variance is specified, both the null and alternative hypotheses are simple hypotheses. Therefore, we can apply the Neyman Pearson Lemma in an attempt to find the most powerful test. The lemma tells us that the ratio of the likelihoods under the null and alternative must be less than some constant *k*:

Now, it's just a matter of finding *k ^{*}*, and our work is done. We want

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.

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!

**State the null hypothesis.** When you state the null hypothesis, you also have to state the alternate hypothesis. Sometimes it is easier to state the alternate hypothesis first, because that’s the researcher’s thoughts about the experiment. (opens in a new window).

Not so long ago, people believed that the world was flat.

Null hypothesis, H_{0}: The world is flat.

Alternate hypothesis: The world is round.

Several scientists, including , set out to disprove the null hypothesis. This eventually led to the rejection of the null and the acceptance of the alternate. Most people accepted it — the ones that didn’t created the !. What would have happened if Copernicus had not disproved the it and merely proved the alternate? No one would have listened to him. In order to change people’s thinking, he first had to prove that their thinking was *wrong*.

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During testing, a scientist may come upon two types of errors. A is when the null hypothesis is rejected when it is true. A occurs when the null hypothesis is not rejected when it is false, according to the University of California, Berkeley.

You’ll be asked to convert a word problem into a** hypothesis **statement in statistics that will include a null hypothesis and an . Breaking your problem into a few small steps makes these problems much easier to handle.

Upon analysis of the results, a hypothesis can be rejected or modified, but it can never be proven to be correct 100 percent of the time. For example, relativity has been tested many times, so it is generally accepted as true, but there could be an instance, which has not been encountered, where it is not true. For example, a scientist can form a hypothesis that a certain type of tomato is red. During research, the scientist then finds that each tomato of this type is red. Though his findings confirm his hypothesis, there may be a tomato of that type somewhere in the world that isn't red. Thus, his hypothesis is true, but it may not be true 100 percent of the time.

The short answer is, as a scientist, you are *required to*; It’s part of the scientific process. Science uses a battery of processes to prove or disprove theories, making sure than any new hypothesis has no flaws. Including both a null and an alternate hypothesis is one safeguard to ensure your research isn’t flawed. Not including the null hypothesis in your research is considered very bad practice by the scientific community. If you set out to prove an alternate hypothesis without considering it, you are likely setting yourself up for failure. At a minimum, your experiment will likely not be taken seriously.

*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.

During a test, the scientist may try to prove or disprove just the null hypothesis or test both the null and the alternative hypothesis. If a hypothesis specifies a certain direction, it is called one-tailed hypothesis. This means that the scientist believes that the outcome will be either with effect or without effect. When a hypothesis is created with no prediction to the outcome, it is called a two-tailed hypothesis because there are two possible outcomes. The outcome could be with effect or without effect, but until the testing is complete, there is no way of knowing which outcome it will be, according to the .

*Figure out the *. The alternate hypothesis is the opposite of the null hypothesis. In other words, what happens if our experiment makes a difference?

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