Testing the Difference Between Two Means (a) identify the clai...

Question

Testing the Difference Between Two Means (a) identify the claim and state Ho and Ha

[APPLET] Migraines

A researcher claims that injections of onabotulinumtoxinA reduce the number of days per month that chronic migraine sufferers have headaches. The table shows the number of days chronic migraine sufferers suffered migraines before and after using the treatment. At , α= 0.01 is there enough evidence to support the researcher’s claim? (Adapted from Journal of Headache and Pain)

Table comparing the number of migraine days before and after treatment for 18 patients.

Accepted Answer

Hello everyone. Glad to have you back. Our next problem says a nutritionist believes that a low carb diet helps individuals reduce their blood sugar levels. To test this, she records the fasting blood sugar levels in milligrams per deciliter of 10 participants before and after 4 weeks on a low carb diet. Assume that mu sub D represents the mean difference in blood sugar before minus after. What are the null and alternative hypotheses for this study? And then we're given 4 different answer choices. A null is mu sub D equals 0, alternative is mu sub D is greater than 0. B null is mu sub D equals 0, alternative mu sub D is less than 0. Cull is mu sub D is greater than 0. Alternative is mu sub D equals 0. Or D, the null is mu subd does not equal 0, and the alternative is mu sub D equals 0. So, let's begin by thinking about the claim here. So our claim. Is that the diet reduces. Blood sugar and we're measuring that by looking at blood sugar levels before and after. And then subtracting the level after from the level before. So if The claim is true. Then our Difference of before and then subtract after. It is going to be greater than 0 because the blood sugar level would have decreased. So that's our claim, and typically our claim becomes our alternative hypothesis, and but key there is that the null hypothesis. Should have a statement of equality. So that would mean it should have an equal sign, a less than or equal to sign, or a greater than or equal to sign. So that's the caveat. The claim is usually alternative, but that no hypothesis needs to have a statement of equality, the status quo that we're testing and will reject or fail to reject. So if our claim Is true, and that would give us this new sub D. Which is that Before minus after value being greater than 0, there are no hypothesis. Will then be that the mean difference m sub D is equal to 0. This would mean that there was no Noticeable change in blood sugar level after 4 weeks on the diet. So that's our null, and then our alternative, we would phrase as mu sub D is greater than 0. So that's going to correspond with choice A. We'll just take a quick look. Is there ways we could have ruled this out more quickly, and there is. We said that the null has to have a statement of equality. So choice C. Where it says muD is greater than 0 would not be an appropriate in null hypothesis. And that's the same with choice D where it says mu sub D does not equal 0. So those are ruled out by that consideration. And then D, choice B, excuse me, has a mu of D equals 0, so that's correct. But it says mu sub D is less than 0. Since we're told mu sub D is the value after subtracted from the value before. If muubD were negative, that would mean that blood sugar level. Increased. So that's not the claim that we're looking at. So you have to be careful in something that involves difference. Make sure you know. How are you coming to that mean difference? Which value is being subtracted from which? Because if we had done a different order of subtraction, we would have that less than sign rather than that greater than sign. So really think that through clearly because this is something where if you were rushing on a test, it would be easy to flip. So once again, we're testing, does a particular diet reduce blood sugar level? Measuring blood sugar levels before and after. And labeling mucub-D the mean difference as the blood sugar level before and subtracting the blood sugar level after to get that difference. And our null and alternative hypotheses is choice A. The null hypothesis is mu sub D equals 0, and the alternative hypothesis is that mu sub D is greater than 0. See you in the next video.

Key Concepts

Hypothesis Testing

Paired Sample t-Test

Significance Level (α)

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