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 5 or more drinks in 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. The college president is interested in testing her suspicion that the proportion of students at her college that binge drink is lower than the national proportion of 0.41 at a level of significance of . Carry out the test and report your conclusion. (round to 2 decimal places, determine the p value – 4 decimal places and report your conclusion.)
Based on the sample of these 462 students calculate .
State the null and alternative hypotheses for this test.
Calculate the Z statistic for the test
What is the probability of getting a Z-value this larger or larger if the null hypothesis is true.
State your conclusion and why.
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