I have been making Excel-based “calculators” to help some of my students who are finding other technology limiting or difficult to use. Currently, I have seven up on this site under the BUS 233 tab. Check them out here. This is the Two-sample z-test for the difference between proportions.
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
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
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
I see many students in my intro statistics courses missing problems related to the normal distribution. One especially common mistake is not using the correct “standard deviation” to find probabilities and percentiles.
Consider the following problem statement:
A bank auditor claims that credit card balances are normally distributed, with a mean of $2870 and a standard deviation of $900.
- What is the probability a randomly selected credit card holder has a card balance less than $2500?
- You randomly select 25 credit card holders. What is the probability that their mean card balance is less than $2500?
- Interpret the two probabilities in terms of the auditor’s claim.
I usually see students get one of the questions correct, but not all. And they either seem to get #1 or #2 correct in about equal proportions. When I inspect their solutions, I find that they get confused over the “standard deviation” to use in the equation for z.
Most students seem to get #1 correct. They use the formula for z: [Read more…] about Normal Distribution Problem- Two Common Mistakes
One way to improve your ability to solve normal distribution problems is to work on recognizing what word problems are requesting you to do.
Consider the following problem statement:
In an investigation of the personality characteristics of drug dealers of a certain region, convicted drug dealers were scored on a scale that provides a quantitative measure of person’s level of need for approval and sensitivity to social situations. (Higher scores indicate a greater need for approval.) Based on the study results, it can be assumed that the scale scores for the population of convicted drug dealers of the region has a mean of 44 and a standard deviation of 7. Suppose that in a sample of 96 people from the region, the mean scale score is x̅ = 46. Is this sample likely to have been selected from the population of convicted drug dealers of the region? Explain. Consider an event with a probability less than 0.05 unlikely. (McClave, Benson, & Sincich, 2014)
First, state the question: How unusual would it be to get a sample mean of 46 if the population mean is 44 and the population standard deviation is 7? [Read more…] about Normal Distribution: Example Problem 1