Question

You are conducting a study to test whether there is a difference in the mean number of alcoholic drinks consumed per evening between the following groups: freshmen who live on campus (sample 1) and freshmen who live off campus (sample 2). Your results will be presented to the Dean of Students so that safety tips and prevention measures can be implemented for the appropriate groups. For freshmen who live on campus (N = 25), their mean number of drinks is 6.2, and their standard deviation is 2. For freshmen who live off campus (N = 30), their mean number of drinks is 3.8, and their standard deviation is
1. Please identify independent variable and dependent variable.

2. Please state in words the null and research hypotheses. Then, present both hypotheses again using statistical notation (note: Please make sure it is the two-tailed test)

3. Which test statistic should you use? (e.g., two sample independent T-test, ANOVA, chi-square, or correlation)?

4.Compute the appropriate test statistic (Note: please show all your work)​

Answer 1

The value of test statistic is 5.45

Data;

• n1 = 25
• n2 = 30
• x1 = 6.2
• x2 = 3.8
• s1 = 2
• s2 = 1

Test Statistic

The formula to calculate the test statistic is given as

$t = \frac{x_1 - x_2}{\sqrt{\frac{s_1^2}{n_1}+ \frac{s_2^2}{n_2} } }$

Let's substitute the values and solve for t

$t = \frac{x_1 - x_2}{\sqrt{\frac{s_1^2}{n_1}+ \frac{s_2^2}{n_2} } } \\t = \frac{6.2 - 3.8}{\sqrt{\frac{2^2}{25} + \frac{1^2}{30} } } \\t = \frac{2.4}{0.44} = 5.45$

The value of test statistic is 5.45

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