An RCT was designed to test the effectiveness of naltrexone, an opiate receptor antagonist, as a treatment for alcohol dependence.  Subjects with chronic severe alcohol dependence were randomly assigned to either 3 months of naltrexone treatment or 3 months of placebo treatment.  The number of drinks per drinking day was compared between the two groups.  Let μ1= population mean number of drinks per drinking day for those on Naltrexone and μ2= population mean number of drinks per drinking day for those on placebo.  The data from the study are summarized in the table below.   Naltrexone (n1 = 196) Placebo (n2=195) Mean Number of drinks per drinking day Xbar1=10.5 Xbar2=9.3 Standard Deviation of Number of drinks per drinking day S1 = 80 S2 = 7.0 The investigators want to test whether there is a significant difference between the two groups using a 5% significance level. 1. What is the most appropriate test to address the investigators’ research question? a. Pearson’s Chi-Squared Test b. ANOVA c. Two-sample t-test assuming unequal variances d. Paired t-test e. Two-sample t-test assuming equal variances   2. Write the correct null and alternative hypothesis for the appropriate test     3. Using one of the probability tables provided to you, compute the p-value corresponding to the test statistic value from part (c) as accurately as possible.  Which range does the p-value fall in? What is your conclusion for the hypothesis test based on this p-value?   a. 0.005 < p < 0.01 b. 0.01 < p < 0.02 c. 0.10 < p < 0.20 d. 0.02 < p < 0.05 e. 0.05 < p < 0.10

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...