True or False? In Exercises 5–10, determine whether the statem...

Question

True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

To support a claim, state it so that it becomes the null hypothesis.

Accepted Answer

Hi, everyone, let's take a look at this practice problem. This problem says a researcher claims that a new teaching method improves student performance. How should this claim be stated in the context of hypothesis testing? So, the first thing we want to do is to write down our claim. And in order to do this, we'll need to define two quantities. The first quantity that we'll define is going to be mu, and this is going to be the mean student performance using the new teaching method. And our other quantity is going to be mute not. And so this is going to be the mean student performance using the traditional method. Now, if we want to see if there is an improvement, we can look at the difference between these two quantities. So if we look at mu minus muk not, in order for there to be an improvement, This quantity needs to be greater than 0 since our Mean student performance for the new teaching method should be larger than the mean student performance for the traditional teaching method, which would make this difference greater than 0. So now we have our claim, we can write down our two hypotheses, or null hypothesis and alternative hypothesis. Now, if we look at our claim here, we see that it contains a strict inequality since we have greater than. And so that means that's going to be our alternative hypothesis. So, our alternative hypothesis, HA is going to be our claim, which is going to be mu minus mu not is greater than 0. And so our null hypothesis, H 0 is going to be the complement of this claim. And so the complement of mu minus mun not being greater than 0 is going to be that mu minus mu knot is less than or equal to 0. And recall that your null hypothesis should have an equality in it. So we either need equal to, less than or equal to or greater than equal to in that statement. And here we have less than or equal to in our statement. So, the answer to this problem is going to be that our null hypothesis, H, is going to be mu minus 0 is less than or equal to 0, and our alternative hypothesis, HA is going to be mu minus is greater than 0, which also happens to be our claim. So this here is the answer that we're looking for for this problem. So I hope that this explanation has been useful, and I'll see you in the next video.

True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

To support a claim, state it so that it becomes the null hypothesis.

Key Concepts

Null Hypothesis

Hypothesis Testing

Claim Support

Watch next