Day 02: Statistics for Business Applications

Roll
Note: homework from chapter 1 is due on Tuesday!
Last time:
- We talked about
  - statistical self-defense - ask questions about methodology!
  - population
  - sample
  - parameter
  - statistic
  - inference
  informally. To see how to write up a problem, we should consult the student webpages for an example.
  As mentioned last time, we want to use complete sentences, and write in complete thoughts when we write up a solution.
- Objectives for chapter 1:
  - In the terms of any example be able to identify the population, sample, parameter, statistic, and statistical inference.
  - Be able to identify examples of descriptive statistics and inferential statistics.
  Remember that associated with inferential statistics are confidence (and significance) levels. The price of more confidence is a better (usually larger) sample.
- Questions about the exercises from Chapter 1
Today: sections 2.1-2.3
- Data come in different flavors:
  - Like peanut butter? - Yes/No
  - What's your height? - some positive real number
  - How was your service? - Poor Okay Excellent
  - What's your favorite soda? - cola, root beer, orange, other
  We're going to knock it down to two types: those for which you can compute averages, and those for which you can't.
  - Quantitative - can compute averages
  - Qualitative - can't compute averages
  Question: How do we identify quantitative data?
  Answer: Quantitative data are real numbers. They are not numbers arbitrarily assigned to represent qualitative data. An experiment that produces qualitative data always asks for verbal, nonnumerical responses (e.g., yes and no; defective and nondefective; Catholic, Protestant, Jewish, and Other).
- Plotting quantitative data
  - How do we look at quantitative data? Example: heights of NKU students.
  - We will focus on the histogram for the visual representation of quantitative data, and specifically the following issues:
    - You should be able to use Minitab to construct a histogram
    - You should be able to interpret a histogram:
      - Describe the shape:
        
        symmetric
        positively skewed
        negatitively skewed
        unimodal
        bimodal
      - What are typical (central) values?
      - What are the largest and smallest values?
      - Are there unusual or atypical values?
  - Let's use Minitab, and see how to create some of these plots with some real data. By the way, you can download a fully-functional version of Minitab for 30-day trial from the Minitab Homepage. Example: Minitab data set from chapter 1.
    - How to load data (datasets for the course are available on your CD, which should have come with the book, but they're also on-line.
    - How to make a histogram
    - Interpreting the Histogram
    - How to change class width
    - Sorting data
    Q: How do I choose the number of classes and the width of the classes to be used in constructing a frequency distribution for a histogram?
    A: Although this choice is arbitrary and no hard-and-fast rules can be given, here are a few useful guidelines:
    1. The classes must be nonoverlapping, so that each measurement falls into exactly one class. Therefore, choose the classes so that no measurement falls on a class boundary (or else create a convention for dealing with cases on class boundaries).
    2. Choose the number of classes to be used as a number between 5 and 20, with smaller numbers of classes being chosen for smaller data sets. Some people use the square root of the number of data.
    3. The approximate width of each class is given by the following:
      Approximate class width = (Largest value - Smallest value)/(Number of classes)
    Choose the actual class width to be a value close to the approximate width that is convenient to work with. Avoid awkward fractional values.
- Statistical self defense:
  
  (from the cover of the Cincinnati Post, Wednesday, January 8, 2003)

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