#### Homework Assignment 2.  Estimation and Hypothesis Testing

General instructions for all assignments – I will deduct points if you do not follow all directions:

• This is NOT a group assignment; your submission should reflect your
• Output from Stata must be provided to earn any credit, and the values that you reference to answer any question must be highlighted in the output. Please do not include the raw data that I provide with each assignment.
• If you are handing in multiple pages, please staple the pages together; I am not responsible for missing pages.
• For each problem that is a hypothesis test, make sure you specify the competing hypotheses, show how you make your conclusion to the hypothesis test, and state the answer to the question!

The data used in this homework assignment is the same that was used in the first assignment.  I still replicate it on Blackboard and call it ‘Data for HW2’.  As a refresher, the data shows annual returns (in %) for 40 small cap corporations and 40 large cap corporations.

1. (35 points)
2. For a 95% confidence interval, what are the lower and upper limits for SmallCaps’s average return?
3. State the competing hypotheses to determine whether SmallCaps’s average return differs from 20%.
4. At the 5% significance level, what is the conclusion to the hypothesis test? Does SmallCaps’s average return differ from 20%?
5. State the competing hypotheses to determine whether the population standard deviation for SmallCaps is greater than 30%.
6. At the 5% significance level, can you conclude that the population standard deviation is greater than 30%?

1. (28 points)
2. State the competing hypotheses to determine whether LargeCaps’s average return is less than 15%.
3. At the 5% significance level, what is the conclusion to the hypothesis test? Is LargeCaps’s average return less than 15%?
4. State the competing hypotheses to determine whether the population standard deviation for LargeCaps differs from 25%.
5. At the 5% significance level, can you conclude that the population standard deviation differs from 25%?

1. (16 points)
2. State the competing hypotheses to determine whether SmallCaps’s average return is greater than LargeCaps’s average return. [These are independent samples; so from the menu select Statistics > Summaries…> Classical tests…> t tests, then in the dialog box make sure to select two-sample using variables (then select the variables), and finally assume unequal variances.]
3. At the 5% significance level, can you conclude that SmallCaps’s average return is greater than LargeCaps’s average return?

1. (21 points)
2. State the competing hypotheses to determine whether the population standard deviation for SmallCaps is greater than the population standard deviation for LargeCaps.
3. At the 5% significance level, can you conclude that the population standard deviation for SmallCaps is greater than the population standard deviation for LargeCaps?
4. Given your answers to questions 3b and 4b, does one type of investing seem superior to the other? Explain.