Factor V is a protein involved in the forming of blood clots. The higher the level of factor V, the faster the blood clots. A Blood Transfusions Service is interested in the effects of sterilization of blood plasma because factor V is unstable and may break down during sterilization. The table below gives measured levels of factor V in blood samples from nine donors. Both pre- and post-sterilization measurements are given for each person. Test whether the mean factor V levels are different post-sterilization. Run the test at a 5% level of significance. Give each of the following  1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. Factor V measurements Donor number Pre-Sterilization Post-Sterilization 1 1025 985 2 1060 1030 3 953 923 4 847 892 5 750 650 6 855 759 7 947 828 8 978 884 9 899 809

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 + ...