The 0.975 number is the probability needed for looking up z-star in tables, or for using the InverseCDF function to get z-star.

The end points of a 95% confidence interval are the points at the ends of an interval that includes the central 95% of the probability in the sampling distribution of the underlying test statistic, but instead of giving those points directly, tables of the sampling distribution give points such that some fraction of the probability will be to the left of any point in the distribution, so to use those tables (or the InverseCDF function) it is necessary to work out those probabilities. For a 95% confidence interval, the end points of the central 95% leave 2.5% the left of the left end point and 2.5% to the right of the right end point, which leaves 97.5% of the probability to the left of the right end point. So to get the end points of a 95% confidence interval, the points that are needed from the table (or from InverseCDF) are the point that gives 2.5%, or a fraction 0.025, of the probability to the left of that point, and the point that gives 97.5%, or a fraction 0.975, of the probability to the left of that point.

So the need for the 0.975 number is simply a consequence of how probability tables and the InverseCDF function work. Tables (and functions like InverseCDF) are based on probability to the left of any point, rather than points that include some probability around the center of the distribution.

The origin of the 0.975 number and is also described, with illustrations, in lesson 16 "Computing Confidence Intervals".

The Wolfram U course Introduction to Statistics is now available with updated content (based on the feedback we received from DSG attendees) and also features a Final Exam. We would like to encourage all our DSG attendees to take the exam and claim their Level 1 certification. Good luck!

Hi everyone! A message to the Statistics Study Group was sent in error at 11:00 CT today. The message reminds you to take the course quizzes for your certificate of completion by Friday, April 28, which is accurate. It also says the exam is available in the framework, which is not accurate. We continue our testing, and the exam will be deployed in the next day or two. We have to ask for your continued patience regarding the exam. We will post here, on Community, when the exam is available.

Keep in mind there is no deadline for taking the exam. Once that is part of the framework, the Level 1 certificate will be available.

Hi @Bob Renninger. Yes, the exam has been added to the framework! Please send bug reports to wolfram-u@wolfram.com. Thank you!

Dear Jose and Arben,

I suspect that there are two errors in the Quiz 6.

Problem 8: There is no correct answer. Multiple choice D) can be an answer but only when it is modified as "Approximately normal and with a standard error of 80g."

Problem 10: There is no answer. Even if we change the order of the two samples in MeanDifferenceCI, still there is no correct multiple choice.

Please see the attached

Attachments:

Quiz 6 Errors.nb

Thank you Arben for your time.

About quizes:

While going through the quizes, it seems that there is no correct option (answer) for Quiz 6, Question 10. I tried with Mathematica and also an specialized statistics software and none of the option correspond to the correct answer for the data supplied.

Quiz 15, Problem 4, What is the expected value of the mean from a sampling distribution of sample size n, drawn from a normally distributed population with standard deviation σ? Goin g through the possible answers provided, the answer that is shown as correct is dependent on the sample problem in the video for nb 44. The central limit theorem governs this situation in this problem and it says the expected value of the mean from a sampling distribution equals the mean (µ) of the population. what you offer is the numerical value of the µ from the specific situation in the sampling problem.

Hi;

When I try to request my final exam from the course framework, nothing happens. I get a wait indicator that never produces a final exam.

Hi;

I am attempting to weight temperature data to use in creating a Normal Distribution using the EstimateDistribution function - see attached notebook. However, it seems that all I am getting is a bunch of messages with the processing failing to create a Normal Distribution. Please tell me what I am doing incorrectly.

Thanks,

Mitch Sandlin

Attachments:

Weighting_Question.nb

I have been experimenting with TTest and I am observing puzzling behavior.

As the attached workbook shows, the SignificanceLevel option does not seem to change the p value for the sample dataset used in Lesson 27.

The attached worksheet also shows experiments where the p value for a TTest with normally distributed data does not seem to decrease as the standard deviation of normally distributed data decreases.

Perhaps I am making a mistake in how I am using TTest command.

Attachments:

TTestQuestions.nb

David,

Thanks for your response. I will need to digest this carefully but I really appreciate your help.

Joe Smith

In the lecture today on the Multiple Testing Problem, a website was mentioned of someone who made it his hobby to collect false positives, or "spurious correlations", e.g., a time series of people drowning in swimming pools over successive years that appears to be very similar to the time series of movies coming out starring Nicholas Cage. The website shows many more funny coincidences.

This is the website: https://www.tylervigen.com/spurious-correlations

There's a book as well by the same author: https://www.amazon.com/Spurious-Correlations-Tyler-Vigen/dp/0316339431

Unfortunately the course framework is not ready for release yet. We are only sharing a beta version with our study group attendees. We can include the link in our reminder emails, so you can get to it, even if you miss the live session.

In the notebook "11.NumericalSummariesOfData.nb" there are images of this kind: You animated these diagrams in the accompanying video and I wondered how you did it. Unfortunately, there are only pictures in the notebook (which makes sense, since you have explanations in the notebook that are "on the soundtrack" in the video). Even if it's a little off-topic, but: would you be so kind and share with us the code of this stunning animation?

Dear Mr. Withoff,

Thank you very much for your answer.

You are absolutely right, the code does distract a lot from the actual topic. There is also a separate course on the topic of "animations" here on WolframU.

Still, thanks for sharing, I found your method of moving the five points or the single point via the join function (pts = ...) very enlightening. Also that you were able to assemble the final image with only "Epilog" was not something I would have expected.

Dear Mr. Sandlin:

I am NO expert on Wolfram or Probability but the following may help you.

Attachments:

Sandlin-solve-pr...nb

How to take the Quizzes and the Online Course Exam?

Show does not work properly in Mathematica 13.2.x. The overlay shown in the downloaded notebook 8.UsingHistogramData.nb fails to show the overlay!

Attachments:

8.UsingHistogramData.nb

There was an update to how temperature units are handled in 13.2. This should provide an explanation: https://reference.wolfram.com/language/tutorial/TemperatureUnits.html

Thank you very much for diagnosing the problem, Rohit! I got a response from support about the units on the x-axis not corresponding between the ListLinePlot and the graphic, and that was also not making sense to me at the time. Your response made it all very clear and, as you indicate, I do not think that this modification in implicit conversion was not documented in the prerelease documents I received for 3.2 or 3.3. It certainly is not compatible with the documentation and is possibly an easily corrected bug.

I truly appreciate your persisting in analysis of this conundrum! I’ll re-report it to Support.

-Marv Schaefer