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Category: Level I Quantitative Methods
Binomial Distribution
Before reading this article, make sure that you have read the article on probability distributions in general. The binomial probability distribution is a discrete distribution: it has only a finite number of possible values that it can take. To understand the binomial distribution, you first have to understand the idea of a Bernoulli trial. A…
Chebyshev’s Inequality
The first thing I’d like to say about Chebyshev’s inequality is that it’s a good thing for most CFA candidates that these exams are written, not oral. If they were oral, most would fail simply because they cannot pronounce “Chebyshev” (or, for that matter, at Level II, “Modigliani” or “heteroskedasticity”). The first part is pronounced…
p vs. α
Candidates galore have problems (nightmares, really . . . but let’s not rub it in) with p-values. I’m here to tell you that understanding p-values is easy. Seriously: easy. A p-value is nothing more nor less than a level of significance, just like α. The best description I’ve heard is that α is the chosen…
Time Value of Money: Using Timelines
Much of finance centers around the idea of the time value of money: a dollar (or euro, or yen, or pound, or yuan, or franc, or won, or ruble, or bhat, or rupee, or whatever) today is worth more than a dollar (or euro, or . . . well, you get the idea) tomorrow, because…
Hypothesis Testing
There are eight articles on hypothesis testing: Synopsis Step 1: State the hypotheses 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 Step 6: Make…
Hypothesis Testing – Synopsis
Hypothesis testing is essentially just an application of confidence intervals: we construct a confidence interval for a particular value, then compute a test statistic and check whether or not it lies in the confidence interval, then do something with that information. There are several steps to hypotheses testing, but in a nutshell it’s just checking…
Hypothesis Testing – Step 7: Make a (Business) Decision Based on the Results of the Test
There are eight articles on hypothesis testing: Synopsis Step 1: State the hypotheses 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 Step 6: Make…
Hypothesis Testing – Step 6: Make a Decision Regarding the Null and Alternative Hypotheses
There are eight articles on hypothesis testing: Synopsis Step 1: State the hypotheses 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 Step 6: Make…
Hypothesis Testing – Step 5: Collect the Sample Data and Calculate the Value of the Test Statistic
There are eight articles on hypothesis testing: Synopsis Step 1: State the hypotheses 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 (you are here)…
Hypothesis Testing – Step 4: State the Decision Rule for Testing the Null Hypothesis
There are eight articles on hypothesis testing: Synopsis Step 1: State the hypotheses 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 (you are here) Step 5: Collect the sample data and calculate the value of the test statistic…