Healthy men aged 21–35 were randomly assigned to one of two groups: half received 0.82 gram of alcohol per kilogram of body weight; half received a placebo. Participants were then given 30 minutes to read up to 34 pages of Tolstoy’s War and Peace (beginning at Chapter 1, with each page containing approximately 22 lines of text). Every two to four minutes, participants were prompted to indicate whether they were “zoning out.” The proportion of times participants indicated they were zoning out was recorded for each subject. The following table summarizes data on the proportion of episodes of zoning out. Group n   S Alcohol 25 0.25 0.05 Placebo 25 0.12 0.03       Calculate a 95% confidence interval for the mean difference between Alcohol and placebo groups.

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 + ...