In order to compare the life expectancies of three different brands of printers, eight printers of each brand were randomly selected. Part of the resulting Analysis of Variance table is presented below: Source of Variation Sum of squares Degrees of freedom Mean square F-statistic p-value Printer Brand ? 2 ? ? 0.0081 Error 770 ? ?     Total 1218 23       We are interested in comparing the mean life expectancies for the three brands of printer using a significance level α = 0.05 .   c. Given the p-value provided in the Analysis of Variance table, decide whether to reject H0 in favour of Ha or to fail to reject H0.  d. Based on your decision in part (c), write your conclusion for the test in the context of the situation. Be specific.

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 + ...