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For all these problems you need to clearly state H0, H1, give… For all these problems you need to clearly state H0, H1, give a (alpha) (if not given), and clearly state your conclusion (in words!).HeightHand64Right70Left63Right61Right69Right68Right68Right75Right71Right1) Use R for all parts of this problem. Use the data on heights you collected a few weeks ago.(a) Do a t-test and test the following:H0: = ?y for your recitation section vs.H1: ? ?yUse a = .01(if, for example, your y = 64.72, then you would do H0: = 64.72)(c) now repeat but subtract 4.75 from your y (so you’d do H0: = 59.97 ( = 64.72 – 4.75))(d) repeat (c) but use a = .00000000001.(You do not need to (and should not) set a in R; make sure you understand why this is true!!) ? Don’t ignore this!!(e) what kind of error did you probably make in part (d)? (Just write out the answer for this question).R instructions:To test, for example, that = 64.72, you need to give R the value of :t.test(height,mu = 64.72)(assuming you named your variable “height”; of course, you may have to do data\$height or something similar depending on how you have your data in R).Since R gives you p-values ( = probabilities) you don’t need to calculate or use t* (although R automatically prints this if you want to use it).MathStatistics and Probability BIOL MISC

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