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 $$\widehat{\mathrm{var}}(Y) = 225$$.

1. 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.

2. What is the standard error of $$\bar{Y}$$?

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

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

5. 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.