Final answer:
A hypothesis test, specifically a one-sample t-test, would determine if college students consume more alcohol than the average American. Using the sample mean, standard deviation, and size, a t-value is calculated and compared with the t-distribution critical value at the 0.05 significance level. This test helps verify if there's a significant difference in consumption habits.
Step-by-step explanation:
The question at hand relates to whether the average college student consumes more alcohol than the average American, which has been stated as 8.7 liters per year. A researcher found that a sample of 51 college students had an average consumption of 9.8 liters of alcohol per year with a standard deviation of 3.9 liters. To test the hypothesis at the 0.05 level of significance, one would typically conduct a one-sample t-test, comparing the sample mean against the population mean.
To perform the t-test, we calculate the t-value using the formula: t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). Given the numbers provided, our t-value would be (9.8 - 8.7) / (3.9 / sqrt(51)), which needs to be compared to the critical t-value at the 0.05 level of significance from the t-distribution table. If the calculated t-value exceeds the critical value, we would reject the null hypothesis and conclude that college students drink more than the average American. Otherwise, we would fail to reject the null hypothesis.
The significance of this analysis is to potentially validate if there is a statistical difference between the average alcohol consumption of the general American population and that of college students. Observing responsible drinking habits is important, and moderation advice suggests up to one drink per day for women and two for men.