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.

# BUS 233

## Confidence Interval for a Mean Given Sigma using StatCrunch

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

## 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

## Normal Distribution Problem- Two Common Mistakes

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