Evergreen State Project Test for Population Proportions Statistics this is Statistics math problems, the questions are post in the attached file, please ch

Evergreen State Project Test for Population Proportions Statistics this is Statistics math problems, the questions are post in the attached file, please check. here is the one link mentioned in the question:https://web.archive.org/web/20150404094832/https://academic.evergreen.edu/curricular/social_dilemmas/fall/Readings/Week_06/milgram.pdf Math 243, Spring ’19, Ostrik
Worksheet 7: Chapters 22, 23 (One- and Two-Proportion Tests)
Grading rubric:
Category
Score Work Description
Engagement – 3pts 0/3 No or almost no meaningful engagement
(Today)
1/3
Few problems attempted and/or limited engagement
3 / 3 Earnest engagement during entire discussion
Clarity – 1pt
0 / 1
At least some of the work is difficult to read
1 / 1 Work is clearly written with minimal erasing or extraneous marks
Completeness – 3pts 0 / 3 The assignment is almost or entirely missing work shown
1/3
The assignment is missing substantial, necessary work
2/3 The assignment has only minor omissions of work shown
3 / 3
The assignment is almost or entirely complete
Accuracy – 3pts 0 / 3 Many answers to exercises are incorrect (or blank)
1/3 Less than half of the answers to exercises are correct
2 / 3 Most answers are completely or almost completely correct
3 / 3 Answers to exercises are completely or almost completely correct
Total – 10pts
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The purpose of this project is to practice tests of significance for a population proportion or difference
between two population proportions using the z statistic, and to reason with the validity of these tests
of significance and confidence intervals.
An infamous experiment (archived PDF located here: https://web.archive.org/web/20150404094832/
http://academic.evergreen.edu/curricular/social_dilemmas/fall/Readings/Week_06/milgram.
pdf) on obedience was conducted by social psychologist Stanley Milgram of Yale University in the sum-
mer of 1961. The experiment consisted of asking a subject (the ‘teacher) to administer increasingly
large electric shocks to another subject in the experiment (the ‘learner’) when the learner failed to
respond correctly to a variety of recall questions. Unbeknownst to the subject, the learner was an actor
and no actual shocks were being delivered. As the voltage increased with intentional) errors by the
learner, a recording of progressively greater pain was played, eventually culminating in complete silence
from the learner at the highest voltages. Whenever the subject showed reluctance to proceed with the
experiment, he was encouraged to continue by the experimenter present in the room.
In anticipation of conducting the study, Milgram surveyed both Yale psychology majors and his psychol-
ogist colleagues to get their predictions. By and large, they believed that almost none of the subjects
would administer the maximum shock of 450 volts, even under the encouragement of the experimenter.
In fact 26 out of the 40 men involved in the study proceeded to administer the highest level of shock
(and not one of the subjects stopped before administering 300 volts).
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Worksheet 7: Chapters 22, 23 (One- and Two-Proportion Tests)
Math 243, Spring ’19, Ostrik
1. Let’s use as a baseline the guesses that Yale majors in psychology made about the proportion of
subjects who would administer the maximum voltage to the learner. In particular, when asked
to identify what proportion of a hypothetical group of subjects would proceed to administer the
highest voltage to the learner, the average response by the psychology majors was 1.2%.
(a) (22.4) Examine the proposal that a significantly higher proportion of individuals in the ex-
perimental conditions would administer the highest voltage punishment, as compared to the
null hypothesis value suggested by psychology majors. Set up hypotheses for the parameter
of interest and compute a test statistic.
(b) (17.6) Explain why the test statistic clearly indicates that we should reject the null hypothesis
and then write what rejecting the null hypothesis means in the context of the experiment.
(c) (22.1) On the second page of the linked document, the section “Methods” with subsection
“Subjects” describes how the subjects for the experiment were found. Does the sampling
procedure illustrated meet with the standards necessary to conduct the significance test from
part (a)?
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Worksheet 7: Chapters 22, 23 (One- and Two-Proportion Tests)
Math 243, Spring ’19, Ostrik
(d) (22.2, 22.3) Find a 99% confidence interval for the proportion of all men who would administer
the maximum shock. Make sure you consider the conditions for which confidence interval are
appropriate given the scenario in question.
(e) (18.1) Based on your confidence interval in part (d), is it reasonable to propose that only
half of all men would administer the maximum shock? Why or why not?
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Worksheet 7: Chapters 22, 23 (One- and Two-Proportion Tests)
Math 243, Spring ’19, Ostrik
2. In 2015, Polish researchers sought to determine if the ‘learner’ role being played by a woman would
change the subjects’ use of the electric shock in situation similar to the Milgram experiment (as
well as whether or not the original American experiment would hold in a European country). In
this Polish experiment, there were fewer and lower levels of shock indicated as compared with the
original Milgram experiment. In the study, all but 6 of the 40 individuals delivered the maximum
shock to the female ‘learner’, while only 2 out of 40 individuals stopped short of administering
the maximum shock when the ‘learner’ was male.
(a) (23.2, 23.3) Compute an appropriate 90% confidence interval for the difference in proportion
of all individuals who would administer the maximum shock to a woman as compared with
the proportion who would administer the maximum shock to a man.
http://dx.doi.org/10.1177/1948550617693060
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Math 243, Spring ’19, Ostrik
Worksheet 7: Chapters 22, 23 (One- and Two-Proportion Tests)
(b) (17.6, 17.8, 23.4) In the article’s conclusion, the authors write “It is worth remarking that
although the number of people refusing to carry out the commands of the experimenter was
three times greater when the student (the person receiving the “shock”) was a woman, the
small sample size does not allow us to draw strong conclusions.” Use an appropriate two
tailed significance test (including writing hypotheses, computing a test statistic and P-value,
and stating a conclusion in the context of the experiment) to confirm this claim.
(c) (23.1) Although our results align with the authors of the study, what about the robustness of
the significance test should make us concerned with the validity of our P-value computation
in part (b)?
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