Please use the following information to answer question 8a & 8b: A random sample of n = 16 scores is obtained from a population with a mean of µ = 45. After a treatment is administered to the individuals in the sample, the sample mean is found to be x̅ = 49.2. 8a. Assuming that the sample standard deviation is s = 8, calculate r2 (MUST SHOW WORK FOR THIS PROBLEM). Note: You must provide calculations for the t-observed statistic, in addition to r2.     8b. Calculate Cohen's d to measure the size of the treatment effect (MUST SHOW WORK FOR THIS PROBLEM).

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 + ...