Question

college students and drinking habits: a public health official is studying differences in drinking habits among students at two different universities. they collect a random sample of students independently from each of the two universities and ask each student how many alcoholic drinks they consumed in the previous week.
sample statistics

	size (n)	mean ($\bar{x}$)	sd (s)
sample 2	49	5.7	1.9

the official conducts a two - sample t - test to determine whether these data provide significant evidence that students at university 1 drink more than students at university 2. the test statistic is t = 2.64 with a p - value 0.005.
which of the following is an appropriate conclusion?
a. the samples provide significant evidence that students at university 1 drink more than students at university 2.
b. the samples do not provide statistically significant evidence that there is a difference in drinking habits at the two universities.
c. we cannot use the t - test in this case because the variables (number of drinks) are likely skewed to the right at each university.

Explanation:

Step1: Recall t - test decision rule

In a hypothesis test, if the p - value is less than the significance level (commonly $\alpha = 0.05$), we reject the null hypothesis.

Step2: Analyze given p - value

Here, the p - value is 0.005 which is less than 0.05. The null hypothesis is typically that there is no difference in the means (i.e., students at University 1 and University 2 drink the same amount on average), and the alternative hypothesis is that students at University 1 drink more than students at University 2. Since the p - value is less than 0.05, we reject the null hypothesis.

Answer:

A. The samples provide significant evidence that students at University 1 drink more than students at University 2.