In this video we're going to talk about the decisions and conclusions of hypothesis testing. We're not really going to talk about making the actual decision, but just the language that we're going to use and then once the decision is made how we're going to phrase that conclusion. Okay so first let's go ahead and recall our two definitions.
We've got the null hypothesis H sub 0 and that's the statement to be tested against, that's our baseline. And then we have the alternative hypothesis. This is our claim, H sub a, and this is what we're trying to gather evidence to support it or not. The language of decisions, so once we have gathered our data and we're ready to assess whether our data supports our claim or not, our decision is really to reject or not reject the null.
So that's what we'll be doing. We'll be saying we reject the null or do not reject the null. Please note that we will never use the word accept.
When we start talking about our errors that we can make when we actually make a decision, we'll talk about why we don't use that word accept. And then just another note that the decision is based on the evidence, so it's not just something that we can randomly assign. Once we've made a decision, we need to write some kind of conclusion.
So we find or do not find evidence to support our... alternative claim. The way that we phrase that is if we reject the null, we will write a conclusion starting, there is sufficient evidence to support the alternative claim. And we don't want to just put H sub a or the alternative claim. We really want to be specific to the problem.
So in our examples, we'll go ahead and fill out what that claim is. And then on the other hand, if we do not reject the null, we say there is not sufficient evidence to support the the alternative claim. And again, we don't want to leave that as notation. We really want to fill in what we have for our claim. Okay, so let's look at an example.
The FDA controls food regulations. On a jar of applesauce, it is labeled as having 64 ounces of applesauce. A consumer thinks that a certain applesauce manufacturer is shorting customers. So part A, we're going to review by just stating the null. and alternative hypotheses.
So that's going to be our H sub zero and H sub a. For the null, we always ask the question, well are we talking about our parameter of mean or the parameter of proportion? So here we're having a label that's marking the number of ounces of applesauce. So that's definitely not a proportion, which means that the average number of ounces of applesauce in each jar.
So that's what we're going to put for the null. The mean is 64, and that's the average number of ounces per jar as it shows on the label. For the alternative, now that we've nailed down our parameter mu, we know that we just have to figure out the sign here. So a consumer thinks that a certain applesauce manufacturer is shorting customers.
So if it's shorting customers, that means that there's actually less applesauce than stated. So we'll put that as mu is less than 64. And again, I just put the wording back there, and that helps us when we write our conclusion. Okay, part B.
In our decision, we reject the null hypothesis, state the conclusion. So let me just review here from our last slide. If the null is rejected, then we do have evidence to support the alternative.
So it's not our conclusion, but it helps us kind of write our conclusion. So we do have evidence to support the alternative. So our conclusion will be there is sufficient evidence to support the claim that the manufacturer of applesauce is shorting customers. One more example. According to the CDC, 15.2% of American adults experience debilitating migraines.
Stress is a major trigger for migraines. A massage therapist feels that she has a technique that can reduce the frequency and intensity of migraines. Part A, state the null in alternative hypotheses.
So the question again, is this a mean or is this a proportion? So because we're talking about 15.2% of Americans, we know that this is a proportion. So our null will be exactly equal to our 15.2%.
But when we write it... We want to write p equals and then the decimal 0.152. And I just again put the language behind there that that's the current proportion of adults that get migraines. If the massage therapist feels that she has a technique that can reduce the frequency, that percentage should go down. So that's our alternative claim.
p is less than 0.152. And that's the proportion decreases with this technique. So the wording behind it I strongly encourage. You won't have to write this in ohm, but it helps you write everything once you get to your conclusion.
Part B, in our decision, we do not reject the null hypothesis. State the conclusion. So again, let me review. If the null is not rejected, then we do not have evidence to support the alternative claim.
So our conclusion is there is not sufficient evidence to support the claim that the massage therapist technique reduces frequency and intensity of migraine. So just a couple little notes before we end this video. Notice that when we make our decision, we always talk about the null hypothesis, more writing our conclusion we write it as if there is support or not support for the alternative