2. Let's consider an alternative experimental design for the buttery keyboard study from Question 3. In this new approach, ve volunteers are each situated in front of a pair of keyboards (one using traditional keys, and one using buttery keys). Over the course of a typing exercise, the users are asked to periodically switch from using one keyboard to the other in an alternating pattern that causes the overall time spent with each keyboard to be the same at the end of the exercise. The results in words-per-nn'nute {'WPM) for these ve individuals are shown in the following table: Classic Keyboard WPM 1 Table Q2: Participant Performance on either classic keyboards or buttery keyboards, reported in words-per-Ininute (WPM). {Note that these are the same values used in Question 1, but that the design of the experiment will change the way these values are interpreted.) (a) Carry out a two-tailed, paired ttest to compare the words per minute typed on the two different models of keyboard. State your hypotheses and show all your work. You may use any of the following facts without verifying them: For a t-distribution with 4 degrees of freedom, PE :1 3.44) = .9369 For a t-distribution with 5 degrees of freedom, P[t 5 3.44) = .9908 For a t-distribution with 9 degrees of freedom, PE 3 3.44) = .9963 The standard deviation of the differences is 5.2 . (Extra space is given on the next page.) (b) How do the results of this new experimental design (introduced in question 2) com- pare to the results of the original experimental design {used in question 1)? Do they suggest different conclusions about the word-per-minute efciency of the two key- boards?I (c) The sample data suggests there is a lot of variability in typing skill from one partic- ipant to the next {even though all participants were selected from a pool of veteran laptop users). With this in mind? between the experimental approach taken in ques- tion 1 and the one used here in question 2, which do you think will he better suited to answer the original study question: do buttery keyboards differ from traditional keyboards in terms of user words-typedperminute? Explain your reasoning