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 (X) SD(s)
sample1 40 6.9 2.3
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 statistics 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.
C) We ca not use the t-test in this case because the variables (number of drinks) are likely skewed to the right at each university.

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

Thus, option A is correct.

The null hypothesis is a typical statistical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.

It is given that , A two -sample t-test is used to determine whether there is significant evidence that students at University 1 drink more than students at University 2.

Here, we use hypothesis theory.

Given that , test statistic (t) is 2.64 and p - value is 0.005

Since, The p-value of the test is very small for all the commonly used significance level. The null hypothesis will be rejected.

Therefore, the samples provide significant evidence that students at University 1 drink more than students at university 2.

So, option A is correct.

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The correct option is (A).

Step-by-step explanation:

A two -sample t-test is used to determine whether there is significant evidence that students at University 1 drink more than students at University 2.

The hypothesis can be defined as follows:

H₀: The students at University 1 does not drink more than students at University 2, i.e. μ₁ ≤ μ₂.

Hₐ: The students at University 1 drink more than students at University 2, i.e. μ₁ > μ₂.

The information provided is:

test statistic (t) = 2.64

p-value = 0.005

The p-value of the test is very small for all the commonly used significance level. The null hypothesis will be rejected.

Conclusion:

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

Thus, the correct option is (A).

c) yes, because of asa or aas