Suppose we are testing the hypothesis H0: p = 0.3 versus H1: p...

Question

Suppose we are testing the hypothesis H0: p = 0.3 versus H1: p > 0.3 and we find the P-value to be 0.23. Explain what this means. Would you reject the null hypothesis? Why?

Accepted Answer

Below there. Today we're gonna solve the following practice problem together. So, first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A survey claims that over 60% of college students prefer digital textbooks to printed ones. A hypothesis test is conducted and results in a P value of 0.002 at a significance level of alpha equals 0.05. Based on this information, which of the following is the correct conclusion? Awesome. So it appears for this particular prong, we're ultimately trying to take all this information that is provided to us by the prom itself, and we're using it to help us choose from our multiple choice answers which of these multiple choice answers is the correct conclusion. So now that we know what we're trying to solve for, let's read off our multiple choice answers to see what our final answer might be. A is reject the null hypothesis. There is strong evidence to support the claim that more than 60% of college students prefer digital textbooks. B is fail to reject the Noel hypothesis. There is not enough evidence to support the claim. C is failed to reject the null hypothesis. There is strong evidence to support the claim that more than 60% of college students prefer digital textbooks. And finally, D is reject the null hypothesis. There is not enough evidence to support the claim. Awesome. So, first off, in order to solve this particular problem, we need to understand that the claim that is currently being made is that over 60% of college students prefer digital textbooks, and the P value, which I'll call PV for short, so P value. From the test it's going to be equal to 0.002 as given to us by the prom itself, and our significance level, which is denoted as alpha, is gonna be 0.05. So alpha is equal to 0.05. So now our first major step to solve this particular problem is we need to set up our hypothesis. So we need to first focus our attention on the null hypothesis, and the null hypothesis is denoted as H0. So once again, H0 is our null hypothesis, and let us know that our null hypothesis states that P. is less than or equal to 0.60, which is 60% written as a decimal, and this is because 60% or fewer students prefer digital textbooks. We now need to consider our alternative hypothesis, which we'll call H1, and our alternative hypothesis states that P is greater than 0.60 because more than 60% prefer digital textbooks. And as a result, as we should see and be able to recall a note, this is a right-tailed test because we are testing for over 60%. So with that said, we can now move to our second step, which we need to recall and use the decision rule. So we need to note that if the P value So if our P value is less than or equal to alpha, then we can reject H0, so I'll put an X next to H0. And if the P value is greater than alpha, then that means it will fail to reject H0. So I'll put A giant capital F next to H 0, so it will fail our null hypothesis. Maybe it's once again H 0 is our null hypothesis. So, with that said, we need to know once again that our P value is 0.002 and our significance level is 0.05, and let us note really quick. That 0.002 is less than 0.05, so that means we can reject the null hypothesis. So that means that our third and final step. Which we can make our final conclusions, we need to note that because we rejected the Noll hypothesis, that means as a result, there is enough evidence to support the claim that more than 60% of college students prefer digital textbooks. So that will mean that multiple choice answer letter A has to be our correct and final answer. And once again, multiple choice letter A states, reject the Noel hypothesis. There is strong evidence to support the claim that more than 60% of college students prefer digital textbooks. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Suppose we are testing the hypothesis H0: p = 0.3 versus H1: p > 0.3 and we find the P-value to be 0.23. Explain what this means. Would you reject the null hypothesis? Why?

Key Concepts

Hypothesis Testing

P-value

Decision Rule for Hypothesis Testing

Watch next