Suppose that, as a researcher, you're interested in the possible interplay between race and face recognition. You choose 75 participants, 15 of whom are of African descent, 15 of whom are of Western European descent, 15 of whom are of East Asian descent, 15 of whom are of Pacific Islander descent, and 15 of whom are of Middle Eastern descent. You let each participant examine a collection of 35 photographs of faces of college students who are African-American. You then test the participant by presenting, on a computer display and one at a time, a sequence of 70 faces (the 35 familiar ones and 35 others). You ask the participant to identify each presented face as being part of the original collection or not part of the original collection. A trial consists of the presentation of a face and the participant's response. One of the measures of how a participant in this experiment performs is the time that the participant takes to make her responses. You decide to record the total time (in seconds) that each participant takes to make all 70 of her responses. These times are summarized here: Sample size Sample variance Sample Group mean African 15 71.4 46.2 Western 15 71.4 38.4 European East Asian 15 68.5 21.7 Pacific Islander 15 68.5 40.3 Middle Eastern 15 73.4 22.2 Suppose that the populations of times for each of the five racial groups represented in this experiment are approximately normally distributed and have the same mean and the same variance. Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place. (a) Give an estimate of this common population variance by pooling the sample variances given. (b) Give an estimate of this common population variance based on the variance of the sample means given.