Data Set 8-3 :From a random sample of 36 college students the following statistics were obtained on the Milligram "Could You Be a Nazi?" shock test. The higher the score on this test the more the person obeys authority: = 300 volts, = 60 volts.
-Look at Data Set 8-3. In Milgram's original study using a cross-section of Americans, the population mean was 285 volts and the population standard deviation was 60. What is the probability of obtaining a mean like that of the college students (or a higher mean) from the population of Americans?
A) 1.50
B) .4332
C) .0668
D) .0987
E) .4013

Question

Quizplus · Accepted Answer

The probability of obtaining a mean of 300 volts or higher when the population mean is 285 volts and the standard deviation is 60 volts can be calculated using the z-score formula for a sample mean. The z-score is $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the values, $z = \frac{300 - 285}{60/\sqrt{36}} = \frac{15}{10} = 1.5$. Looking up 1.5 in the z-table gives the area to the left, so we subtract this value from 1 to find the area to the right, which represents the probability of obtaining a mean of 300 volts or higher. This calculation gives a probability of approximately 0.0668, indicating a relatively low chance of obtaining such a high mean by random chance from the population of Americans.

Data Set 8-3 :From a Random Sample of 36 College