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Author: Bill Campbell
Hypothesis Testing – Step 2: Select the Appropriate Test Statistic
There are eight articles on hypothesis testing: Synopsis Step 1: State the hypotheses Step 2: Select the appropriate test statistic (you are here) Step 3: Specify the level of significance Step 4: State the decision rule for testing the null hypothesis Step 5: Collect the sample data and calculate the value of the test statistic…
Hypothesis Testing – Step 1: State the Hypotheses
There are eight articles on hypothesis testing: Synopsis Step 1: State the hypotheses (you are here) Step 2: Select the appropriate test statistic Step 3: Specify the level of significance Step 4: State the decision rule for testing the null hypothesis Step 5: Collect the sample data and calculate the value of the test statistic…
Normal Distribution
Before reading this article, make sure that you have read the article on probability distributions in general. The normal (or Gaussian) probability distribution is arguably the most important continuous distribution used in probability and statistics; it is certainly the most important continuous probability distribution appearing in the CFA curriculum. There are several reasons for its…
Degrees of Freedom
Suppose that, for reasons known only to yourself and your therapist, you need to know the average height of all giraffes in the world. Desperately. You face a number of obstacles, not the least of which is that there are estimated to be about 80,000 giraffes in the world, and giraffes are notoriously difficult to…
Student’s t-Distribution
Before reading this article, make sure that you have read the article on probability distributions in general. The Student’s t-distribution has an interesting history. It was developed by a gentleman who worked for Guinness Breweries in Dublin, Ireland, who used it for statistical tests on the ingredients for Guinness beer; apparently Guinness preferred that their…
Confidence Intervals
A confidence interval is nothing more than a range in which we hope (and, with some probability, expect) some value to lie. For our purposes, the values for which we will construct confidence intervals will be parameters for probability distributions. Specifically, we’ll construct confidence intervals for: The mean of a (given) probability distribution (population) An…
Simple Cash Flow Statement
A useful skill to develop is that of writing out a quick, simple, general cash flow statement. Here is an example that you should be able to reproduce in 10 – 15 seconds during the exam: \begin{align}&\ \ \ \ \ \ Cash\ Flow\ from\ Operations\ (CFO)\\ &+\ Cash\ Flow\ from\ Investing\ (CFI)\\ &\underline{+\ \…
Simple Balance Sheet
A useful skill to develop is that of writing out a quick, simple, general balance sheet. Here is an example that you should be able to reproduce in 10 – 15 seconds during the exam: \begin{align}&Current\ Assets\\ &PP\&E\\ &\underline{Intangible\ Assets}\\ &=\ Total\ Assets\\ \\ &Current\ Liabilities\\ &\underline{\ Long-term\ Liabilities}\\ &=\ Total\ Liabilities\\ \\ &Capital\ Stock\\…
Adjusting the Allocation of an Equity/Fixed Income Portfolio using Equity/Bond Futures
Adjusting Allocation Only Adjusting the allocation of a portfolio that comprises both equity and fixed income is nothing more than a combination of: Adjusting the value of the equity portion of the portfolio by a given amount (up or down), and Adjusting the value of the fixed income portion of the portfolio by that same…
Durbin-Watson Statistic (Test)
The Durbin-Watson (DW) statistic is used in a test for serial correlation of residuals (i.e., error terms) in several types of regression models: Simple regression models Multiple regression models Time-series trend models DW is not appropriate for testing for serial correlation of residuals in autoregressive (AR) models. The CFA curriculum doesn’t specify exactly why DW…