The Harvard College Alcohol Study finds that 67% of college students support eff

Question

The Harvard College Alcohol Study finds that 67% of college students support efforts to "crack down on underage drinking." The study took a sample of almost 15,000 students, so the population proportion who support a crackdown is very close to p = 0.67.† The administration of your college surveys an SRS of 120 students and finds that 84 support a crackdown on underage drinking.

If in fact the proportion of all students on your campus who support a crackdown is the same as the national 67%, what is the probability that the proportion in an SRS of 120 students is as large or larger than the result of the administration's sample? (Use a Normal approximation with a continuity correction to approximate the probability. Round your answer to four decimal places.)

Explanation / Answer

We first get the z score for the critical value:          
          
x = critical value =    83.5      
u = mean = np =    80.4      
          
s = standard deviation = sqrt(np(1-p)) =    5.150922248      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    0.601833973      
          
Thus, the right tailed area is          
          
P(z >   0.601833973   ) =    0.273642329 [ANSWER]

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