Performing a Wilcoxon Test In Exercises 3–8,
a. identify...

Question

Performing a Wilcoxon Test In Exercises 3–8,

a. identify the claim and state H0 and Ha.

[APPLET] Calcium Supplements and Blood Pressure In a study testing the effects of calcium supplements on blood pressure in men, 12 men were randomly chosen and given a calcium 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 α = 0.01, can you reject the claim that there was no reduction in diastolic blood pressure? (Adapted from The Journal of the American Medical Association)

Accepted Answer

Hello, everyone. Let's take a look at this next question. A researcher claims. That using a new meditation technique will decrease the stress levels of participants. A sample of 10 participants had their stress levels measured before and after using the technique. The researcher believes that stress levels will decrease. What is the claim and what are the null and alternative hypotheses. And we have answer choices of a. The claim is stress levels decrease. Null hypothesis, median difference equals 0, alternative hypothesis, median difference is less than 0. Choice B, the claim stress levels increase. The hypothesis median difference is greater than 0, alternative hypothesis median difference is less than 0. Do I see claim stress levels remain the same? null hypothesis, median difference does not equal 0. Alternative hypothesis median difference is less than or equal to 0. And I'll scroll up a little to read Jo D. Which is that the claim as stress levels decrease, the null hypothesis is median differences less than are equal to zero, and the alternative hypothesis is that median difference is not equal to 0. So, first of all, two of these can be eliminated quite easily. We are told twice that the researcher claims that the new technique will decrease the stress levels. So, we would want one of our choices to be stress levels decrease, and only A and D say that. Choice B says that stress levels increase, so that would not be our claim, and then Choice C says stress levels remain the same, also not our claim. So our claim is definitely going to be that stress levels will decrease. So what does that mean for our null and alternative hypotheses? So, we have 2 possible results, well, 3 possible results. They can increase, decrease or stay the same. But If we use the median to structure our hypotheses, we can exclude the values that don't any results where there's no change, and then we have only two results, increase or decrease, to consider in our test. So in a problem like this, our null hypothesis, we will make that about the median. And recall that what we're testing is, will stress levels will be affected? Will they decrease? So our null hypothesis is going to be that there's no change, that the median is equal to 0. So why don't we say that, you know, why don't we oppose it with like median is. Greater than are equal to 0. Well, because setting the median equals equal to 0 means that we can treat the probability of our stress levels decreasing as being 0.5. It gives us a known probability because if the median is zero, then assuming our null hypothesis is true, we're equally likely. To have a result above the median or below the median. P is equal to 0.5. So. Even without looking further, we can see that in choice A, we do have the median being difference being equal to 0, and when we scroll down to choice D, it says median difference is less than or equal to 0. So, that will be incorrect and choice D will therefore be incorrect. So, let's scroll back up here. But last of all, we're asked for the alternative. Hypothesis. So our alternative hypothesis. Also going to be about the median, and since the claim is that meditation will decrease the stress levels, We would say that the median difference then. And we'll go ahead, we should have said median difference in the null hypothesis, but the median difference between stress. After and stressed before will be less than 0. Since that claim is that the stress will go down. And so that does give us our answer choice of choice A, just for, you know, curiosity's sake, note that this means we would use a Wilcoxen. Signed rank test with that fairly small sample size and it would be left tailed. With that less than symbol there. But we don't necessarily need to know that. All we're asked for again is our claim. So, our answer is choice A, the claim being that stress levels decrease, and then we had to find our null and alternative hypotheses. So, our null hypothesis is that the median difference is equal to 0. Well, our alternative hypothesis is that the median difference is less than 0. See you in the next video.

Key Concepts

Wilcoxon Test

Hypothesis Testing

Significance Level (α)

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