A study is done to determine whether switching laptops to use " butterfly"-style keyboards(where keys are almost flat and sink only slightly when pressed) affect the number of words typed per minute. A pool of 10 long-time laptop users is split at random into two groups of size n=5. One group uses a traditional keyboard for a typing exercise, and the other group carries out the same typing exercise using a butterfly keyboard. The results are collected and shown below: Classic Keyboard WPM: 41, 70, 25, 63, 58 Butterfly Keyboard WPM: 36, 62, 20, 58, 41 (a) Carry out a two-tailed, independent samples t-test to compare the words typed by the two groups. State your hypotheses and show all your work. You may use geogebra to help out with computations for this problem.per minute (b) Why was it important to split the participants into two groups at random? Suppose,instead, that the pool of 10 individuals were allowed to voluntarily seat themselves in a room containing 5 butterfly-style keyboards and 5 traditional keyboards. (Suppose they knew in advance that they'd be performing a typing task.) Speculate as to possible biases that could arise from this non-random assignment.

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