Day 02: STA205 - Introduction to Statistical Methods

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Today:

First "quiz grade": your first assignment, which will be turned in for grading on Thursday, 8/30, is the following:
- Prepare exercises #8, 9, p. 34 from section 2.3, as well as the review exercise #7, p. 49 from chapter 2.
- Fully interpret the histograms, and write up your work nicely, using a word processor.
- One of these (chosen randomly) will be collected.
- To help you, a couple of handouts:
  - StatCrunch ~ Creating Word Documents
  - StatCrunch ~ Histograms and Descriptive Statistics
Questions over problems from homework?
Review of Chapter 1 -- what is statistics?
Review of Section 2.1 - Two types of data
Section 2.3 (cont.): Plotting quantitative data using the Histogram
- Review:
  - Histograms communicate the relative importance of different intervals of the measured data, using counts per interval
  - Construction:
    1. range of the data broken into convenient, non-overlapping "intervals" of equal width
    2. count how many values are in each interval -- the "frequency" of an interval
    3. On a set of axes, rectangles are drawn above the intervals to a height equal to the frequency.
  - We can use StatCrunch to construct them, but it takes a human to interpret them....
- How does changing Bin Width change the look of the histogram?
- Example: heights of NKU students.
- Interpreting a histogram:
  - Features that describe the shape of a histogram:
    - symmetric
    - right (positively) skewed
    - left (negatively) skewed
    - bimodal versus unimodal
    - other(!) -- e.g. multimodal...
    (What are some examples that would give rise to skewed distributions?)
  - What are typical values?
  - What are central ("average") values?
  - What are the largest and smallest values (range)?
  - Are there unusual or atypical values?
- Creating histograms using StatCrunch and the data from our book.
  - Our book used another package -- Minitab -- to do the statistics. Reference is often made to data sets, e.g. exam02-04
  - To use that data in StatCrunch, you would load the data from the web, using the name http://www.nku.edu/~statistics/data/exam02-04.xls
  - You can also paste in data, if you have it from some other source.
- The interpretation of a histogram should be written up using a word processer, and should look professional. One of our goals for you in this course is as follows:
  For any assignments or homework exercises that are collected students will create a neatly presented word document. This document will always include:
  - Supporting StatCrunch analyses that are copied into the document.
  - Well written, grammatically correct, sentences for any interpretations or explanations.
Section 2.4: Populations, Samples, and Inferences
- Definitions:
  - Population: a population is the collection of all the data that could be observed in a statistical study
  - Sample: a sample is a collection of data chosen from the population of interest.
  - Inference: an inference is a decision, estimate, prediction, or generalization about a population based on information contained in a sample from that population.
- Example: Heights of NKU students
Section 2.5: Random Sampling
- Definitions
  - random sample: Consider sampling n observations from a population. If every collection of n observations has the same chance of being selected, then the sample is random.
  - convenience sampling: If the observations selected for a sample are those that are easiest to obtain, or are selected because they are simply available, the sample is haphazard or convenient. (examples, p. 41)
  - volunteer sample: If a survey is presented to people in such a way that each individual must take the initiative to reply, the response or opinions form a self-selected or volunteer sample.
- Example: Heights of NKU students

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