Algebra II.4.D.27 - Ruling Out Chance – Exit Ticket

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4 questions

Read the description below and answer the following questions.

In the Exit Ticket of a previous lesson, an experiment with 20 subjects investigating a new pain reliever was introduced. The subjects were asked to communicate their level of pain on a scale of 0 to 10 where 0 means no pain and 10 means worst pain. Due to the structure of the scale, a patient would desire a lower value on this scale after treatment for pain. The value “ChangeinScore” was recorded as the subject’s pain score after treatment minus the subject’s pain score before treatment. Since the expectation is that the treatment would lower a patient’s pain score, a negative value would be desired for “ChangeinScore.” For example, a “ChangeinScore” value of -2 would mean that the patient was in less pain (for example, now at a 6, formerly at an 8). In the experiment, the null hypothesis would be that the treatment had no effect. The average change in pain score for the treatment group would be the same as the average change in pain score for the placebo (control) group.

The alternative hypothesis would be that the treatment was effective. Using this context, which mathematical relationship below would match this alternative hypothesis? Choose one.

Follow the directions below.

With reference to the randomization distribution below and the inequality in your alternative hypothesis, compute the probability of getting a Diff value as extreme as or more extreme than the Diff value you obtained in the experiment.

Based on your probability value from Problem 3 and the randomization distribution above, choose one of the following conclusions: a. Due to the small chance of obtaining a Diff value as extreme as or more extreme than the Diff value obtained in the experiment, we believe that the observed difference did not happen by chance alone, and we support the claim that the treatment is effective. b. Because the chance of obtaining a Diff value as extreme as or more extreme than the Diff value obtained in the experiment is not small, it is possible that the observed difference may have happened by chance alone, and we cannot support the claim that the treatment is effective.

From EngageNY.org of the New York State Education Department. Grade Algebra II Mathematics Module 4, Topic D, Lesson 27. Internet. Available from https://www.engageny.org/resource/algebra-ii-modul...; accessed 21/Apr/2016.