**Due:** Turn in hard copy at the beginning of class on
Monday, Oct. 23.

You have to answer Question 1, but you can choose either Question 2 or 3 to turn in.

**Question 1: Coding Exercises from Chapter 4:** 1

**Question 2: Coding Exercises from Chapter 5:** 1

**Question 3:** Let \(Y\) denote the height of an oak tree in
feet. Suppose that you have the theory that \(\mathbb{E}[Y] = 50\). You are able to
collect a random sample of 100 observations of oak tree heights. Using
this data, you calculate \(\bar{Y} =
63\) and that \(\widehat{\mathrm{var}}(Y) = 225\).

Calculate a t-statistic for testing the null hypothesis that \(\mathbb{E}[Y]=50\) (for the test, set the significance level to be 5%). Do you reject the null hypothesis here? Explain.

What is the standard error of \(\bar{Y}\)?

Calculate a p-value for the null hypothesis that \(\mathbb{E}[Y]=50\). How do you interpret it?

Calculate a 95% confidence interval for \(\mathbb{E}[Y]\). How do you interpret it?

Now suppose that you change the significance level to be 1%. How does this change your answers to parts (a)-(d); to discuss part (d), provide a 99% confidence interval.