Picking Alpha: The cost of Type I and Type II Errors-2

Earlier this year, I read of the analysis of the recent fatality caused by an Uber autonomous car in Arizona. (Lee, 2018) It occurred to me (and others) that this terrible situation is possibly related to Type I and Type II errors. (Efrati, 2018)  A Type I is a false...

One-sample Sigma Known z-test for the Mean

Joel, I have not checked all your calculations, but the process you used looks good. I note that this is a problem where you are given a lot of raw data. Which technology did you use? I ask because problems where you have to manually enter a lot of raw data often lead...

How to State the Conclusion about a Hypothesis Test

After you have completed the statistical analysis and decided to reject or fail to reject the Null hypothesis, you need to state your conclusion about the claim. To get the correct wording, you need to recall which hypothesis was the claim. If the claim was the null,...

Simple One-sample z-test for the Mean when Sigma is Known

Here is a way to do a simple one-sample z test when we know the population standard deviation sigma. If this was a left tail test as indicated by an < in the alternative hypothesis, the standardized test statistic (z) of -1.753 falls in the rejection region below...

Empirical Rule Cheatsheet

Empirical Rule percentiles are the percentage of data below (to the left of) an x value. Use this Quick and Easy calculator to find percentiles when you are given the population mean and standard deviation and x values. In most intro stats classes, you will only be...