Stating the Null and Alternative Hypotheses In Exercises 25–30...

Question

Stating the Null and Alternative Hypotheses In Exercises 25–30, write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.

Base Price of an ATV The standard deviation of the base price of an all-terrain vehicle is no more than $320.

Accepted Answer

Hi, everybody. Let's move on to the next problem. A company asserts that the standard deviation of the delivery times for their packages does not exceed 2.5 days. Choose the correct null and alternative hypotheses and indicate which states the claim. And then we have different conditions in our four answer choices, or different different null and alternative hypotheses and claims. We'll look at those a little more closely after we work out our problem, rather than read them aloud twice. So, first, let's start with what is the company saying? So, it says the standard deviation does not exceed 2.5 days. So we'll put clean. Standard deviation of sigma, so it does not exceed, that means it must be less than or equal to. 2.5 days. Always be alert to language that means there's an equality there. So when we try and state our null hypothesis, we remember that that defines the status quo, and more importantly, that null hypothesis has some element of equality there. So the null hypothesis. Should have Equals less than or equal to or greater than or equal to. So, since we have that sigma is less than or equal to, we're going to make that our null hypothesis. So, our null hypothesis will be sigma is less than or equal to 2.5. So if that's the case, then our alternative hypothesis. Just needs to be That sigma is greater than 2.5. And then we can see that. No hypothesis is the one that states the claim. can is slightly less common, usually our hypothesis will. And then often the claim is the alternative hypothesis. Well that No hypothesis is the status quo, but again, the. No hypothesis needs to have that equality symbol in this case, it is. Part of that less than or equal to there. So, when we look at our answer choices for the one that matches, we have choice A, null hypothesis is sigma greater than 2.5. Alternative hypothesis, sigma less than or equal to 2.5, and the claim is the null hypothesis. So, this is incorrect. Cross out, I say. Choice B says null hypothesis is sigma less than or equal to 2.5. Alternative hypothesis is sigma greater than 2.5, and the claim is a null hypothesis. So this does match, so B will be our answer. And then we already have our answer, but just to be complete, choice C says null hypothesis, sigma greater than or equal to 2.5. Alternative sigma less than 2.5 and claim is alternative hypothesis, so that's not correct. And then choice D null hypothesis is sigma equal to 2.5, alternative hypothesis, sigma not equal to 2.5, and claim alternative hypothesis. So, this is not correct. So again, we have to pick the correct null alternative hypotheses and indicate which states the claim. And our answer is choice B. That are No hypothesis says sigma is less than equal to 2.5. Alternative hypothesis, sigma greater than 2.5, and the one that represents the claim is the null hypothesis. See you in the next video.

Key Concepts

Null Hypothesis (H0)

Alternative Hypothesis (H1)

Hypothesis Testing

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