The following is used for questions 10 to 13 . A tencher proposes a course designed to increase reading speed (measured by words per minute). To evaluate the effectiveness of this course, the teacher tests students before and after the course. The result is following: Student 1 2 3 4 Speed before class 100 160 120 | 167 | 200 Speed after class 136 170 135 169 210 Assume that the reading speeds are approxirmately normally distributed. Let ua be the mean difference between two populations (i.e., Hd = Hbeforz- Hafter).

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 + ...