Saturday, March 21, 2020

Sampling Distributions, Central Limit Theorem and Confidence Intervals

Comic of the Day
Tip: The things themselves are all right, so who cares?
Announcements and Deadlines
Labs 6, 7, 8 and 10 due Thu Apr 16
Excel Final Exam on Thu Apr 16
Chapter 6-8 assignment (Moodle) due Thu Apr 23
Theory Exam (Chapter 6-8) is combined with Chapter 12 exam and will be on Thu Apr 23
This Week

 1. Sampling Distributions and Central Limit Theorem

Central Limit Theorem Simulator

Set n=25 and run the simulator several hundred thousand times. 
For any population distribution (normal, uniform, skewed, custom), the distribution of the sample mean, x̄, is normally distributed with the following properties:


  • the mean of the sample means approaches the population mean





  • the standard deviation of the sample means is less than the population standard deviation (it actually follows the formula below)

    • Lab 8 - Sampling Distributions
    Lab 8 shows how a sample mean, x̄ (n=16 or 100) is usually close to a population mean, µ (N=10,000), and gets closer as n increases.  You will use a VLOOKUP function to randomly sample from your payroll data.

     3. Confidence Intervals
    "A Mainstreet Technologies poll ... suggests Albertans are highly resistant to any tax hikes. Only 15 per cent of survey respondents say they’d favour increased taxes. Spending cuts are the preferred solution of 43 per cent."
    "...automated phone survey of 3,184 Albertans."
    "The Mainstreet Technologies survey is considered accurate within plus or minus 1.7 percentage points, 19 times out of 20."

    Confidence Interval for Population Proportion, p

    Confidence Interval for Population Mean, µ (σ known)

    Confidence Interval for Population Mean (σ unknown)

    For More Information
    Confidence Intervals (videos go beyond the content of this course)
    Confidence Intervals (small sample size)

    Next Week - Linear Equations and Graphs, Lab 10 - Linear Regression
    Pre-read notes on Moodle
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    Thursday, March 19, 2020

    Lab 7 - Normal Distributions

    Comic of the Day
    Tip: We might all be a little out of practice, so go easy on us?
    Announcements and Deadlines

    Production Assignment 2 assessments and peer/self evaluation due Sun Mar 22
    Chapter 6-8 assignment (Moodle) due Mon Mar 30
    Theory Exam (Chapter 6-8) postponed until further notice
    This Week - Lab 7 - Normal Distribution
    Lab instruction video on Moodle
    Mobius questions


    Next Week - Lab 8 - Sampling Distributions
    Lab instruction video and Mobius questions are already posted
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    Thursday, March 12, 2020

    Lab 6 - Probability

    Comic of the Day
    Tip: Watch your syntax when using the =FRIENDIF() function

    Applications of Visualizations
    Dashboard

    Understand statistics, don't BE a statistic


    Prevention
    To help protect you and your family against all respiratory illnesses, including flu and COVID-19, you should:

    • Wash your hands often and well
    • Avoid touching your face, nose, or mouth with unwashed hands.
    • Avoid close contact with people who are sick
    • Clean and disinfect surfaces that are frequently touched
    • Stay at home and away from others if you are feeling ill
    • Contact your primary health provider or Health Link 811 if you have questions or concerns about your health
    • When sick, cover your cough and sneezes and then wash your hands
    Announcements and Deadlines
    Production Assignment 2 assessments and peer/self evaluation due Sun Mar 15
    Chapter 6-8 assignment (Moodle) due Mon Mar 30
    Theory Exam (Chapter 6-8) in class Mon Mar 30

    Drop-in tutorials will run every Tue 12-12:50 in CAT286 (computer lab)

    Today - Lab 6 - Probability
    See videos on Moodle
    Activity 1 is related to injury rates in your individual data sets
    In Activity 2 you will create a binomial probability distribution related to injury rates, and then also create a model for workplace injuries using random number generation in Excel.  Excel's built-in Binomial Distribution function with the following syntax:
    BINOM.DIST(x,n,p,false)


    Next Lecture - 7.1-7.3 Sampling Distributions and Central Limit Theorem
    Pre-read 7.1-7.3 in the textbook
    Watch this 10:41 primer video on the Central Limit Theorem
    https://www.khanacademy.org/math/ap-statistics/sampling-distribution-ap/sampling-distribution-mean/v/sampling-distribution-of-the-sample-mean

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    Wednesday, March 11, 2020

    6.2 Applications of Normal Distributions

    Comic of the Day
    Tip: Always make the diagram match one on our z table

    Unit 2 Exam (out of 25 marks)
    µ=64.3%
    σ=20.5%
    median=66%
    60% within µ±1σ
    Unit 1 Exam (was changed to out of 25 marks instead of 30)
    µ=58.1% 69.7%
    σ=18.4% 22.1%
    median=60% 72%
    70.0% within µ±1σ

     For students who scored 100% on Mobius chapter 1-4 assignments:
    µ=75.8% on Unit 1&2 Exams

    For students who scored <100% on Mobius chapter 1-4 assignments:
    µ=51.8% on Unit 1&2 Exams

    Announcements and Deadlines
    Production Assignment 2 assessments and peer/self evaluation due Sun Mar 15
    Chapter 6-8 assignment (Moodle) due Mon Mar 30
    Theory Exam (Chapter 6-8) in class Mon Mar 30

    Drop-in tutorials will run every Tue 12-12:50 in CAT286 (computer lab)

    Today - 6.2 Applications of Normal Distributions
    Notes on Moodle
    z-score calculator



    Next Lecture - Lab 6 - Probability
    Watch the video tutorial and try it on your own

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    Monday, March 9, 2020

    6.1 Standard Normal Distribution

    Comic of the Day
    Tip: It's not that scary if you practice

    Explanation of Grading for Production Assignment 1
    Submission Grade (ave 29.9/40) - instructor graded

     Individual Contribution (ave 8.9/10) - based on the Peer and Self Evaluation ratings, comments, and my observations

     Assessment Grade (ave 8.0*/10) - based on how close you graded the group versus how I graded the group, and also on the quality of your comments (specific and insightful)

    * students who did not assess other groups were assigned a grade of zero and were not included in this average

    Announcements and Deadlines
    Production Assignment 2 assessments and peer/self evaluation due Sun Mar 15
    Chapter 6-8 assignment (Moodle) due Mon Mar 30
    Theory Exam (Chapter 6-8) in class Mon Mar 30

    Drop-in tutorials will run every Tue 12-12:50 in CAT286 (computer lab)

    Today - 6.1 Standard Normal Distribution
    Notes on Moodle
    z-score calculator

    For More Information
    Normal distribution


    Next Lecture - 6.2 Applications of Normal Distributions
    Pre-read notes on Moodle

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    Thursday, March 5, 2020

    Feedback from PA1

    Feedback from PA1
    - read the rubric carefully and make sure you are meeting all the criteria (e.g. whether it's a table or a chart, what the rows/columns should be, how much/little information to include, what Excel functions/features should be enabled like a Filter)
    - who is your intended audience?  An email to a front line supervisor should be short and to the point.  For PA2, a briefing report for senior management should have a little more substance but be careful not to include redundant sentences just to "flower things up"
    - the analysis has to be correct!  In PA1 you needed to correctly count the number of employees in each category (never trained, expired, will expire and by each training type).  For PA2 you will need to use correct data for all of your charts.

    Suggestions for PA2
    - double-check that you haven't missed any data or counted anything twice
    - each chart should have a clear message and a reason why you have included it
    - three mandatory charts (raw data, histogram, ogive)
    - two or more additional charts (e.g. pie, stacked column, boxplot) that focus on overexposures, other contributing factors or changes over time
    - do not include your names anywhere.  If you need a name you are Saif T. Guy.  In the workplace you will have to be careful not to violate employee privacy and accidentally include their name on an injury report!

    Remember:
    Under no circumstances should you be sharing your files (including the raw data files) with other groups, and under no circumstances should you open files from other groups.
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