]]>

Here is another MSL problem where you really have a lot to key in because there are 30 sample values each with 5 digits to enter.

I worked it in Excel and would like to point out two other things:

- One key is to recognize you are given the population standard deviation, sigma, so you should use the z-test.
- You must recognize the claim and state it both in words and math symbols. If you do that correctly, then doing the math become easier as does writing the conclusion.

Here, because we have a right-tail test, we must subtract the values we get from the tables or basic Excel functions from 1. Failing to recognize this results in the many, many mistakes I see in student quizzes with a P-value that is the wrong tail.

And if you know which hypothesis the claim is, writing the conclusion becomes a lot easier.

I would also note that in the image, I show how to get Excel to use the basic logic of hypothesis tests to “make” the Reject or Fail to Reject decision automatically using Excel functions AND and IF. On the calculators on my website, I take it one more step and get Excel to write the conclusion too. This is not difficult to do if you want to create your own Excel calculators which you can then use on quizzes and exams.

]]>

If the claim was the null, then your conclusion is about whether there was sufficient evidence to reject the claim. Remember, we can never prove the null to be true, but failing to reject it is the next best thing. So, it is ** not correct** to say, “Accept the Null.”

If the claim is the alternative hypothesis, your conclusion can be whether there was sufficient evidence to support (prove) the alternative is true.

Use the following table to help you make a good conclusion.

The best way to state the conclusion is to include the significance level of the test and a bit about the claim itself.

For example, if the claim was the alternative that the mean score on a test was greater than 85, and your decision was to *Reject then Null*, then you could conclude:

“**At the 5% significance level, there is sufficient evidence to support the claim that the mean score on the test was greater than 85.**”

The reason you should include the significance level is that the decision, and thus the conclusion, could be different if the significance level was not 5%.

If you are curious why we say “Fail to Reject the Null” instead of “Accept the Null,” this short video might be of interest: Here

]]>]]>

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:

]]>At any rate. 8.1.11, the difference between two means hypothesis test standardized test statistic requires µ

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:

]]>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:

First, most of us need time to reflect on what we have read and perhaps go back and re-read the material or read supporting material [you can also apply this concept to material you have watched.] I’m guessing that all of us have had instances of where we leave a discussion/argument with less than satisfactory results only to have the “perfect” response pop into our minds later after we mull over the discussion. Similarly, I have no doubt that we all have had the experience of coming up with a solution to a problem after we “sleep” on it. That same thing happens to me a lot when I ponder how to solve a complex stats problem.

There is an analogy in sports/exercise. Recall the “burn” in muscles we all experience when we begin to learn a new sport/exercise which uses muscles differently then we are used to using them. We are told to space our exercise to allow our muscles time to recover. (Bishop & Woods, 2008) We are well advised to space our exercise at least 48 hours including a good night’s sleep if at all possible. Same for studying stats, in my opinion. (Kapur, 2014)

Second, there is good research that shows better results in math-like courses occur when students use spaced-repetition, which is nothing more than having time between their work sessions on topics. (Cepeda, Pashler, Vul, Wixted, & Rohrer, 2006) That is one reason I always recommend my students space their work over the course of the week, beginning early in the week, and not delay “everything” for a crashed pace on the weekend.

Finally, there is the fact that this is an online course which limits the student-student and student-instructor interactions which I believe are important in most difficult topics. I took a few online courses during my doctorate, but they were not really parallel to this course because I could still see and talk to my classmates and instructor at school the following days to rehash what went on in the online course. I have tried holding Google Hangouts in my online courses but find that only a small portion of the class can participate each time I try to hold them. And some of my students complained that the Hangouts were unfair to them because their work/life did not allow them to attend regardless of when I scheduled the Hangouts. Viewing the video of the hangout did not satisfy their need for interaction the way actual attendance would. But my sense is that if all my courses were 15-week terms, it is more likely that every student would be able to attend some of the weekly/twice-weekly hangouts. And that would be materially beneficial.

My opinion based on my observations (admittedly anecdotal evidence) in teaching stats for seven years is that adult students with all their family and job responsibilities do better (learn more with less stress) in 15-week terms. Period.

Bishop, P., & Woods, A. (2008). Recovery from training: a brief review. *Journal of Strength and Conditioning Research*, 22(3):1015-1024.

Cepeda, N., Pashler, H., Vul, E., Wixted, J., & Rohrer, D. (2006). Distributed practice in verbal recall tasks: A review and quantitative synthesis. . *Psychological Bulletin*, 132:354-380. Retrieved from UCLA College of Life Sciences.

Kapur, M. (2014). Productive failure in learning math. *Cognitive Science*, 38(5): 1008-1022.

Silve, E., & White, T. :. (2015). *The Carnegie Unit: A Century-Old Standard in a Changing Education Landscape.* Standford: Carnegie Foundation for the Advancement of Teaching.

]]>

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.

(Larson & Farber, 2015, p. A16)

Larson, R., & Farber, B. (2015). *Elementary Statistics: Picturing the World, 6th.* Boston: Pearson.

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.

]]>