Download a PDF with the step-by-step instructions for finding the confidence interval for a population mean, μ, using StatCrunch.

## Empirical Rule and Chebychev’s Theorem

Excel calculator for problems involving the use of the Empirical Rule or Chebyshev’s Theorem:

2.4 Empirical Rule and Chebyshev Theorem

## “Easy” Excel Inverse Triangular Distribution for Monte Carlo Simulations

Back in the dark ages when access to computers was not all that common, I was faced with developing a project schedule for, to me, a complex construction project. I was not that long out of school, so I sought out my boss with the hope he would give me some guidance on how to approach the problem.

He told me to use three-point estimation and to talk to some of the older engineers in the firm to get their ideas on the likely outcomes. So, I did and learned that the three points he was talking about were the worst case, the best case, and the most likely case for what would happen during the project. (Wikipedia, n.d.)

He also directed me to consider using PERT. I did and learned that form of project management scheduling including consideration of the optimistic time estimate (o), the most likely or normal time estimate (m), and the pessimistic time estimate (p). In PERT, instead of using probabilities for each estimate of the time required, the task time is calculated as (o + 4m + p) ÷ 6. (Taylor Jr., 2011)

To model a three-point estimate with a probability distribution you need to use a triangular distribution. Today, three-point estimates are commonly used in business and engineering, so it is somewhat surprising that Excel does not have a built-in function to help. I was recently faced with this dilemma in my quantitative methods course which I am trying to migrate away from expensive software solutions. [Read more…] about “Easy” Excel Inverse Triangular Distribution for Monte Carlo Simulations

## Paired samples are not always obvious

Although we often think of paired samples as being the same person (thing) in a “before” and “after” treatment setting, there are some other important types of paired samples.

One kind are “natural” pairings, such as spouses, siblings, and especially twins. This type of pairing is often used in medical observational research when it is difficult to construct a true experiment. (PennState, 2017)

But even more common are other types of pairing. A more accurate label for this two-sample test is a test for *dependent *samples. Samples are dependent when there is a relationship of some kind in play which causes the samples to not be independent.

I like this definition from the Minitab blog:

If the values in one sample affect the values in the other sample, then the samples are dependent. [Read more…] about Paired samples are not always obvious

## Chi-square Goodness of Fit test

Consider the following problem:

A research firm claims that the distribution of the days of the week that people are most likely to order food for delivery is different from the distribution seen in the past. You randomly select 494 people and record which day of the week each is most likely to order food for delivery. The table below also shows the results of your count. At alpha, α, = 0.05, test the research firm’s claim.

This sounds like a test of Goodness of Fit between the historical pattern and the observed pattern.

The claim is that the actual pattern and the historical pattern are different. That means we need the inequality math operator, which, in turn, means the **claim is the alternative hypothesis**.

Stating our two hypotheses: [Read more…] about Chi-square Goodness of Fit test

## Are rabbits normal?

This is a great video on the normal curve and the central limit theorem.