Evergreen State Project Test for Population Proportions Statistics

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Mathematics

The Evergreen State College

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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


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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 10 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). 2 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)? 3 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? 4 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 5 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)? 6
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Explanation & Answer

Attached you will find the outline (table of contents) and answers of your assignment in Word and PDF. The equations were made using the Microsoft Office Equation Editor. Please let me know if you need edits 😊

ANSWERS. PROJECT. TEST FOR POPULATION PROPORTIONS.
PART 1.
A) The average response by the psychology majors represents the percentage or proportion (1.2% or 3 men
of 250, 𝑝̂1 = 0.012) that we want to compare with the experimental data (26 of 40 men involved in
the study administered with the highest level of shock, 𝑝̂ 2 = 0.650) using statistics. The null
hypothesis establishes that there is no significant difference between the proportion made by
psychology majors and the experimental proportion:

Hypotheses
Null Hypothesis
Ho: 𝑝̂ = 𝑝̂ 0
Alternate Hypothesis
Ha: 𝑝̂ ≠ 𝑝̂0
Test Statistics (z-test)
𝑧=

𝑝̂ − 𝑝̂ 0
√𝑝̂ 0 (1 − 𝑝̂0 )
𝑛

=

0.650 − 0.012
√0.012(1 − 0.012)
40

= 37.058

B) We should reject the null hypothesis because the value of z-test is related with a p-value of 1.000,
meaning that practically, with a confidence level very close to 100%, both proportions are significantly
different between each other. In the context of the experiment, the proportion proposed by psychology
majors is significantly different from the proportion reflected by the experimentation.
C) A condition to use the z-test is that we need independent random sample for experimental group, either
from random sampling or a randomized experiment. The sampling methodology selected the
participants by a newspaper advertisement (volunteer sample) and direct mail solicitation (convenience
sample). Both sampling methodologies could result in bias due the lack of representativeness of the
sample with the population, even if the men selected believed that they are going to ma...


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