In Exercises 7–10, the statement represents a claim. Write its...

Question

In Exercises 7–10, the statement represents a claim. Write its complement and state which is Ho and which is Ha.

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Accepted Answer

Hello everyone. Let's take a look at this question together. A scientist claims that the population mean temperature is not equal to 98.6 °F. Write the complement of this claim and indicate which is the null hypothesis and which is the alternative hypothesis. So in order to solve this question, we have to recall how to determine the complement of a claim. So that we can write the complement of the claim that the population mean temperature is not equal to 98.6 °F, and then identify our null hypothesis and our alternative hypothesis. And so the first step in writing the complement of the claim is to understand the claim that we are given, which the scientist claims that the population mean temperature is not equal to 98.6 °F. And this claim can be written as mu does not equal 98.6. Well, since this is a not equal to statement, we know it goes into the alternative hypothesis, and since we have our claim, we can write the complement of the claim, which the opposite or the complement of mu does not equal 98.6. We know is mu does equal 98.6. So we have our claim and our complement of the claim, and now we can assign these statements to our different hypotheses, which we know claims involving not equal to less than or greater than our alternative hypotheses because they represent a change from the status quo, and we know the null hypothesis always includes such as equal to, less than or equal to or greater than or equal to. Therefore, from our information, we know the null hypothesis is given as mu is equal to 98.6, and our alternative hypothesis is given as mu does not equal 98.6, which this matches the scientists claim. So we have our null hypothesis, and our alternative hypothesis, and looking at our answer choices, we can identify that answer choice A is the correct answer, as it contains the correct null and alternative hypotheses, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

In Exercises 7–10, the statement represents a claim. Write its complement and state which is Ho and which is Ha.

μ<33

Key Concepts

Null Hypothesis (H0)

Alternative Hypothesis (Ha)

Complement of a Hypothesis

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