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Five Steps in a Hypothesis Test

The central limit theorem comes in a variety of flavors, but generally stated says that the sampling distribution of the mean will be a normal distribution with a theoretical mean equal to mu and a theoretical standard deviation, called the standard error, equal to sigma of the model of scores divided by the square root of the sample size.

Notice one other thing about Edgington's definition. Hesaid

When you about a , you can use your test statistic to decide whether to reject the null hypothesis, H0. You make this decision by coming up with a number, called a -value.

In statistics, we always assume the null hypothesis is true.

In a quality control situation, the mean weight of objects producedis supposed to be 16 ounces with a standard deviation of 0.4 ounces.A random sample of 70 objects yields a mean weight of 15.8 ounces. Isit reasonable to assume that the production standards are beingmaintained?

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.

Then, make a decision based on the available evidence.

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.

We rejected the null hypothesis, i.e., claimed that the height is not 65, thus making potentially a Type I error. But sometimes the p-value is too low because of the large sample size, and we may have statistical significance but not really practical significance! That's why most statisticians are much more comfortable with using CI than tests.

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Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

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!

Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

[We can also note that normalcdf(-1E99,0.475,0.5,.0193) = 0.0976,or about 10%. Basically, if Ho is true, the probability of obtainingthe sample proportion 48% is about 10%. We don't have "strong"evidence to reject Ho. And, we are simply saying that itis not unreasonable to assume that the population parameter is 50%.]

Type I = you are innocent, yet accused of cheating on the test.

A value is a probability associated with your critical value. The critical value depends on the probability you are allowing for a Type I error. It measures the chance of getting results at least as strong as yours if the claim (H0) were true.

Type II = you cheated on the test, but you are found innocent.

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

Null hypothesis, H0: 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.

against the alternate hypothesis

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).

Specify the hypothesis: H0: μ = 65 HA: μ ≠ 65

Analysis: The population involved is the means of randomsamples of size 70 chosen from a population with mean = 16 andstandard deviation = 0.4. Call this population P. The Central LimitTheorem says that the distribution of P is normal, that the mean of Pis 16, and that the standard deviation of P is 0.4/Ã(70) = 0.048. Asworded, this is a 2-tail situation. The null and alternate hypothesesare, respectively

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