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5. A statistics instructor with a strong dislike of whiteboards wishes to determine whether there's evidence to support the claim that students are better able to engage with mathe- matics on blackboards. As one component of the study, the instructor decides to evaluate whether students perform better on math problems when either white font is used against a black background (blackboard, or BB setting) or black font is used against a white back- ground (whiteboard, or WB setting). The instructor develops a Mobius quiz for students, using a set of questions that are behaved to be equally challenging, but calibrata Mobius to present half the questions in WB style and half the questions in BB style. To remain neutral, the instructor makes no assumption about which style will be better. The overall performance by students on each coloring scheme is recorded below: | Student BB performance | WB performance Table Q5: Student Test Performance on Questions Presented in either Blackboard (BB) or Whiteboard (WB) colors. (a) Carry out an independent samples ttsst comparing the mean grades for the two presentation styles. Use a signicance threshold of o: = .05. State all relevant sample statistics, hypotheses, and test statistics/distributions, as well as the pvalue and ap- propriate conclusion of the test. (b) Carry out a dependent samples t-test using the student-by-student dierences in grade across conditions. Use a signicance threshold of a = .05. State all relevant sample statistics, hypotheses, and test statistics/distributions, as well as the p-value and appmpriate cenclusiOn of the test. (c) Why might the tests in part a) and part b) reach different conclusions? Discuss What is being tested in each case, and suggest which of the two tests you nd more appropriate for this experiment