In anticipation of conducting the study, Milgram surveyed both Yale psychology m

Question

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 subjectswould 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). https://web.archive.org/web/20150404094832/http://academic.evergreen.edu/curricular/social_dilemmas/fall/Readings/Week_06/milgram.pdf

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%.

Explanation / Answer

Let p be the population proportion of men involved in the study proceeded to administer the highest level of shock and not one of the subjects stopped before administering 300 volts.

Given that,

x = 26

n = 40

Confidence level (C) = 99% = 0.99

99% confidence interval for p is,

p^ - E < p < p^ + E

where p^ is sample proportion

E is margin of error

E = Zc * sqrt (p^ * q^) / n

where Zc is critical value for normal distribution.

q^ = 1 - p^

We can find this confidence interval in TI-83 calculator.

steps :

STAT --> TESTS --> A: 1-PropZInt --> ENTER --> Input all the values --> C-level : 0.99 --> Calculate --> ENTER

99% confidence interval for p is (0.45574, 0.84426)

We are 99% confident that population proportion is lies between 0.45574 and 0.84426

Now in the next part we have to check whether only half of all men would administer the maximum shock.

That is here proportion is 0.5 which is lies between 0.45574 and 0.84426.

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