Create a vector of 30 random draws from a N(5,9). Explain why the hypothesis test H0: μ = 5 HA: μ ≠5 might be reasonable here. What objects discussed so far in this question live in the unknowable world? In the knowable world?
a) Create a 90% confidence interval for XÌ„. Show the formula you used and justify your assumptions. Interpret this confidence interval.
b) Carry out the hypothesis test above with α = 0.1, and explain any assumptions you make. Draw the approximate null distribution for this hypothesis test by hand, as we have done in class. What is this the distribution of?
c) Draw the rejection and acceptance regions on your distribution. Relate the acceptance region to the set of values in your confidence interval from part a). What if we didn't know the data were drawn from N(5,9)?
d) Repeat parts b) and c) for the following hypothesis test H0: μ = 6 HA: μ ≠6. Compare and interpret your results for both hypothesis tests. What if you did not know the true distribution of the data? Use R coding language to answer.