Identifying Type I and Type II Errors In Exercises 31–36, desc...

Question

Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis test of the indicated claim.

Video Game Systems A researcher claims that the percentage of U.S. gamers that are women is not 50%.

Accepted Answer

Hello 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 school administrator claims that the proportion of students who prefer online classes is not 60%. For this hypothesis test, describe the meanings of Type 1 and type 2 errors. Awesome. So it appears for this particular problem, we're asked to use a hypothesis test for this particular claim, which the claim is that the proportion of students who prefer online classes is not 60%, and we're also asked to describe the meanings of Type 1 and Type 2 errors. So we're trying to solve for two separate answers for this particular problem. So now that we know what we're ultimately trying to solve for, let's take a moment to read off our multiple choice answers to see what our final answer pair might be, noting that I'm going to read the answer for Type 1 error first and then the answer for Type 2 error second. So A is conclude the proportion is 60% when it is not, and conclude the proportion is not 60% when it is. B is conclude the proportion is less than 60% when it is 60%, and conclude the proportion is greater than 60% when it is 60%. And C is, conclude the proportion is not 60% when it is 60%, and conclude the proportion is 60% when it is not. And finally, D is conclude the proportion is greater than 60% when it is not, and conclude the proportion is less than 60% when it is not. Awesome. So our first step that we need to take in order to solve this problem is we need to state our hypotheses, starting with the null hypothesis first, which will denote as H 0. So the null hypothesis for this particular problem, as we should recall, states that P is equal to 0.6, because that's 60% written as a decimal, which will mean that our alternative hypothesis, HA will state that P cannot equal 0.6. Where P, in this case, is the proportion of students who prefer online classes. Moving right along here. Our second step is we need to focus on the type 1 error, which I'll call T1 for short. So focusing on the type one error, we can reject the null hypothesis when the null hypothesis is true, which will put a capital T to remind us that we can reject the null hypothesis when the null hypothesis is true, meaning we need to conclude that the proportion is not 60% when it is 60%. And our third step focusing on the type 2 error, we fail to reject the null hypothesis when the null hypothesis is false, so I'll put a capital F for false as a reminder to us, meaning we can conclude the proportion is 60% when it is not 60%. So with that in mind, based on the information we've collected together, that will mean that our final answer without a doubt, will have to be multiple choice answer letter C, which once again states Type 1 conclude the proportion is not 60% when it is 60%, and type 2, conclude the proportion is 60% when it is not, and that's it, we've officially solved for this problem. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis test of the indicated claim.

Video Game Systems A researcher claims that the percentage of U.S. gamers that are women is not 50%.

Key Concepts

Hypothesis Testing

Type I Error

Type II Error

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