According to the National Institute on Alcohol Abuse and Alc

According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA), and the National Institutes of Health (NIH), 41% of college students nationwide engage in “binge drinking” behavior, having five or more drinks on one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college that binge drink is lower than the national proportion. In a commissioned study, 462 students are selected randomly from a list of all students enrolled at the college. Of these, 162 admitted to having engaged in binge drinking. Based on the P-value for this test, which of the following statements is TRUE?

We should conduct the study again because the P-value is too extreme.

We should accept the null hypothesis based on this P-value.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.41
Ha:   p   <   0.41
As we see, the hypothesized po =   0.41      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.350649351      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.022882156      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.593752475      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.00474674      

Thus, P < 0.01.

Therefore,

OPTION B: In over 99% (1-0.01) of the samples that we might collect, we would not observe results more extreme than the observed proportion of binge drinkers from this sample. [ANSWER, B]