1) 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: \begin{aligned} &\mathrm{H}_{0}: \mu=\bar{y} \text { for your recitation section }\\ &\text { vs. } \quad \mathrm{H}_{1}: \mu \neq \bar{y} \end{aligned} \text { Use } \alpha=.01 \text { . } (if, for example, your y = 64.72, then you would do Ho: µ = 64.72) (c) now repeat but add 4.75 to your y (so you'd do Ho: µ= 69.47 ( = 64.72 + 4.75)) (d) repeat (c) but use a=.00000000001. (You do not need to 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 here) R instructions: To test, for example, that u= 64.72, you need to give R this value. Just do: 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). The instructions for confidence intervals were given in a previous homework assignment(remember that R defaults to a 95% confidence interval). 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).

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