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.
10
1.
The alternative hypothesis would be that the treatment was effective. Using this
context, which mathematical relationship below would match this alternative
hypothesis? Choose one.
The alternative hypothesis would be that the treatment was effective. Using this
context, which mathematical relationship below would match this alternative
hypothesis? Choose one.
10
2.
Follow the directions below.
Follow the directions below.
10
3.
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.
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.
10
4.
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.
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.