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 given x values whose z-scores are are integers. If a problem has x values whose z-scores are not integer values, you can find percentiles using the Normal tab on the workbook. If you would like a copy of this workbook, email me at drdawn@TheStatsFiles.com and let me know you have subscribed to my YouTube channel.

## Pick-a-Problem: What difference does it make? 8.1.27

Question: The problem I struggled with this week is 8.1.27. It seemed like all the rest of the problems in the first chapter, but I got it wrong because I used “0” instead of the µ1-µ2 value. Not sure when I am supposed to use that value or how it is determined. I used the “view an example” feature to figure out I was supposed to put it in there for the homework, but I am worried about the quiz and not being able to recognize the situation it is needed.

Answer: When we are comparing two samples, whether means or proportions pay close attention to the claim. Here, the claim is that the difference in the two mean salaries is more than $5000. That requires the claim to be the alternative hypothesis since “more than” is a > operator, which is an inequality. So, Ha: μ_{1} – μ_{2 }> $5000.

I know. You are saying that you don’t see a claim. But when a problem asks a question as this one does, that is the claim to be tested unless you find a more definitive claim later in the problem.

Note that you need to follow the “standard” format which is that we consider μ_{1}– μ_{2 }and not the reverse because that is the way the claim is stated in the problem: Region 1 is mentioned before Region 2. I think it might be less confusing if the problem had compared Alabama and Florida salaries, but the first entity (population) mentioned is logically μ_{1}.

Here is the StatCrunch solution: [Read more…] about Pick-a-Problem: What difference does it make? 8.1.27

## Pick-a-Problem: Not given values for µ in 8.1.11

Question: I have hit the wall on a simple problem. I seem to be hitting these more often now.

At any rate. 8.1.11, the difference between two means hypothesis test standardized test statistic requires µ_{1} – µ_{2}. So, how does one calculate this when we are never given a value for μ? I used 0 for the values, and came out with the WRONG answer. Request a nudge in the right direction.

Answer: James, for most of our mean difference problems, we will not be given the assumed population means or the mean difference. If not, you use 0 for the mean difference. In your problem, you are told that μ_{1} = μ_{2}, so the mean difference μ_{1} – μ_{2}, is 0.

Here is the StatCrunch solution with slightly different summary data:

## 8 vs 15-week Intro Stats Courses

Yes, this is a demanding course for most people. My strong sense is that it, like other statistics courses, should only be taught in the 15-week format. I say that knowing the strong preference among adult students for 8-week or shorter courses they can more quickly check as “Completed” on their degree To Do list.

We need to remember that regionally-accredited degree programs require courses to satisfy the Carnegie credit system in which a credit-hour represents the equivalent of 3 student work hours per week for 15 weeks. (Silve & White, 2015) Thus, this 3-credit-hour course must require 9 student work hours per week in the 15-week format, which equates to about 17 hours per week in the 8-week format.

Again, my strong sense is that most adult students rationalize “they” can get the work done in less time either consciously or subconsciously. And that can lead to stress when the inevitable work/life issues occur which disrupt our plans. I believe that this type of added stress does not help people learn.

A second reason I believe this quant course should be taught in only 15-week terms is that stats is a subject in which time is needed to process and to really learn the concepts. There are two aspects of this: [Read more…] about 8 vs 15-week Intro Stats Courses

## Technology vs Tables and Rounding Mistakes

Joe,

Two important points you bring up:

- Do not round intermediate values in a string of calculations. Wait until the very last step/answer to round to the number of decimals required by MyStatLab. On this problem and many others in this course, rounding too early can lead to wrong answers.

In the instructor view, I can cycle through the variations of that problem different students might see. On about half, I could round the z value to two decimal places and still get the correct answer. But for the one shown, I get the wrong answer. On all of them, if I round the standard error, sigma x-bar, to three decimal places, I always got the wrong answer. Rounding early is tempting if you are using a calculator and writing down the intermediate values instead of storing them in the calculator’s memory, if that is possible for your calculator.

- All tables today are created using technology, not the reverse. So do not delude yourself into thinking the tables are more accurate. If you enter the normal table on this problem with the rounded z of -2.02, you will get the wrong answer unless you interpolate between the table values. Note: on some problems where MyStatLab does not tell you to use the tables, it
**may**accept the nearest table value (intersection of highlights). But if the problem says, “Use technology,” the approximate table value will be counted wrong.

[Read more…] about Technology vs Tables and Rounding Mistakes

## Chebychev’s Theorem Excel Calculator

Because it is not often used, save in intro stats courses, and is relatively simple to calculate, most stats software programs (StatCrunch included) do not have a special tool to help. Instead, you will need to manually recreate the formula using Excel or a calculator. To make the process easier, I have built an Excel calculator which makes typical intro stats problem quick and easy. This is a short video from my YouTube channel, The Stats Files, giving a quick review of Chebychev’s and showing how to use the Excel calculator: https://youtu.be/8rtb2gYjwzs

If you send an email to drdawn@thestatsfiles.com telling me you have subscribed to my YouTube channel, I will send you a copy of the workbook. [Read more…] about Chebychev’s Theorem Excel Calculator