In Exercises 1–6, use a sign test to test the claim by doing t...

Question

In Exercises 1–6, use a sign test to test the claim by doing the following.

a. Identify the claim and state H0 and Ha.

[APPLET] In a study testing the effects of an herbal supplement on blood pressure in men, 11 randomly selected men were given an herbal supplement for 12 weeks. The table shows the measurements for each subject’s diastolic blood pressure taken before and after the 12-week treatment period. At , can you reject the claim that there was no reduction in diastolic b

Table displaying diastolic blood pressure measurements before and after treatment for 11 patients.

Accepted Answer

All right. Hello, everyone. So this question says, a researcher wants to determine whether a new meditation routine lowers anxiety levels. A group of 10 participants has their anxiety scores measured before and after 1 month of meditation. The researcher believes the routine reduces anxiety. You are asked to test this claim using the sign test. What is the claim and what are the known alternative hypotheses? So, first, what do we understand about the situation? Well, in this case, the study involves paired data. Because we're making a comparison between data points measured before and after an intervention, in this case, the meditation. So, the researcher believes that the after score is going to be lower than the before score, because the researcher believes that anxiety is going to be reduced after the routine. So What that means Is that most of the differences, according to the researcher's claim, should be negative. In other words, the after. Subtracted by the before. Anxiety scores should be less than 0. Now we define the claim. Again, the researcher claims that the meditation routine reduces anxiety. Which means that the after scores. Should be less than the before scores for most people. Thus supporting that the differences should mostly be negative. And so the number of negative signs in this test should be greater than the number of positive signs. And now we can set up the hypothesis. Remember that the sign test is checking whether or not there is a difference in the direction of the changes, whether that's positive or negative. So the hypotheses are going to be based on the median of the differences, or of the direction of science. So, To restate here The claim is that the routine. Reduces Anxiety. And so the null hypothesis. That's H knot Would state that the median difference. is equal to 0, which means that there is no change in anxiety levels before and after. The alternative hypothesis, or H so one on the other hand, represents the claim and is. Different from the null hypothesis, so. The alternative hypothesis would state instead. That the median difference. is less than 0 in accordance with the claim that anxiety is decreased after the meditation. And there you have it. So now here is the complete answer. And with that being said, thank you so very much for watching, and I hope you found this helpful.

Key Concepts

Sign Test

Hypothesis Testing

Paired Samples

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