Identifying H0 and H1
In Exercises 5–8, do the following...

Question

Identifying H0 and H1

In Exercises 5–8, do the following:

a. Express the original claim in symbolic form.

b. Identify the null and alternative hypotheses.

Landline Phones Claim: Fewer than 10% of homes have only a landline telephone and no wireless phone. Sample data: A survey by the National Center for Health Statistics showed that among 16,113 homes, 5.8% had landline phones without wireless phones.

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 recent study claims that fewer than 15% of college students commute to campus by bicycle. In a survey of 2500 students, 12% reported biking as their primary mode of transportation. A, express the original claim in symbolic form. B, identify the null and alternative hypothesis. Awesome. So it appears for this particular problem we're asked to solve for two separate answers or technically 3 separate answers. Our first answer is we're asked to express the original claim in symbolic form for Part A. And for Part B, we're trying to solve for two separate answers. We're trying to identify the null hypothesis, that's our first answer, and the alternative hypothesis. So those are our two answers for Part B that we're trying to solve for. So now that we know we're ultimately trying to solve for, let's start to solve for part A first. So focusing our attention on part A first. We need to express the original claim in symbolic form. So first off, let us call P lowercase p, to represent the proportion of college students who commute by bicycle, and since the claim is fewer than 12%, Once again, music it says that Oh sorry, not 12%. So we're told that 12% reported biking as their primary mode of transportation, but we're told that fewer than 15% of college students commute to campus by bicycle. So, since the claim, and let's underline this, since it's important, since fewer than 15% of college students commute to campus by bicycle, that means we could state that P. is less than 0.15, because if we take 15% and we divide it by 100, we get 0.15%, which is 15% written as a decimal, and that is our first answer. Hooray, we did it. We solved for our first answer. So now, we could start solving for part B. Fantastic. So focusing your attention on part B now. We now need to identify the null and alternative hypotheses. So we need to know to solve for the null hypothesis, we need to note that it will always contain equality. So that will mean that for the null hypothesis, so let's call this H0. So H0, the null hypothesis will state that P is equal to 0.15. And similarly, so for the alternative hypothesis, as we should recall, which we'll call this H1, and the alternative hypothesis, as we should recall, reflects the claim, the initial claim, so that will mean that H1, our alternative hypothesis, will state that P is less than 0.15. And that's it. That is our final set of answers. Hooray, we did it. To quickly recap what we've learned, our final answers without a doubt for Part A state that the claim is P is less than 0.15, and for B H 0. P is equal to 0.15, and for H1, P is less than 0.15. 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.

Key Concepts

Null Hypothesis (H0)

Alternative Hypothesis (H1)

Symbolic Representation

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