Chapter 1--Sampling and Descriptive Statistics



STATISTICS 301—APPLIED STATISTICS Fall 2008

Chapter 0--Intro.Doc

STATISTICS 301—APPLIED STATISTICS, Statistics for Engineers and Scientists, Walpole, Myers, Myers, and Ye, Prentice Hall

Brain Aerobics Pop Quiz

1. You are competing in a linear race and overtake the runner in second place. In which position are you now?

a. first b. second c. third d. fourth e. cannot be determined

2. Suppose you have 40 blue socks and 40 brown socks in a drawer. If you reach into the drawer without looking at the socks, what is the smallest number of socks you must take out to make sure that you have a pair of socks of the same color?

a. 2 b. 3 c. 4 d. 40 e. 41

3. A doctor’s son’s father was not a doctor. How is this possible?

GOAL:

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BASIC TERMS AND DEFINITIONS

Statistics Science of collecting, summarizing, analyzing, and interpreting data (information, usually in the form of numbers).

Three major parts of Statistics:

I. Producing/Collecting Data Sampling and Experimental Design.

II. Descriptive Statistics Summarizing data.

III. Inferential Statistics Analyzing and interpreting data and drawing conclusions.

The analysis depends on how the data was collected.

Inferential Statistics is built on top of some ideas in Probability.

Probability Field of mathematics involved with determining the relative frequency of certain events.

Thought processes involved in Probability and Inferential Statistics:

Probability - Deductive thought process (known facts imply new facts.)

This is analogous to selecting some elements from a box with known contents and asking “what are the chances of getting certain results?”

Inferential Statistics - Inductive thought process (observations are used to infer properties).

This is analogous to selecting some elements from a box with unknown contents and making a guess about the totality of the contents of the box.

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Basic (most important) terms in Statistics (Language of Statistics)

Population Collection of all elements (individuals or items) under consideration.

Unit An individual element of the population.

Variable A measurement or characteristic of a unit. (Types of data.)

Parameter A numerical characteristic (descriptive summary measure) of the popln.

Some common parameters are: population mean = (

population variance = (2

population standard deviation = (

population proportion = p

Sample A part of the population from which information is obtained.

Statistic A numerical characteristic (descriptive summary measure) of a sample.

Some common statistics are: sample average = [pic]

sample variance = s2

sample standard deviation = s

sample proportion = [pic]

EXAMPLES

In the examples that follow determine: the population, parameter, sample, and/or statistic.

EXAMPLE #1

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EXAMPLE #2

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EXAMPLE #3

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EXAMPLE #4

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EXAMPLE #5

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Distributions

The concept of distribution in statistics is at the very core of all of statistics. Simply put a distribution is the set of all values of some measurement. Here are a couple of pictures of two distributions.

Grade Distributions in STA 261 and STA 671.

How do these two distributions differ?

|[pic] |

| [pic] |

How about a single “distribution?” How would you summarize this distribution?

|[pic] |

Distribution = Center

Spread

Shape

More on Shape

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Modality

Skewness/Symetry

Bell-Shaped/Normal

Outliers

Goal of Statistics

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1. Investigate feature(s) of a single distribution

2. Compare feature(s) of two (typically more!) distributions.

|[pic] |[pic] |

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Some Final Comments on Distribution.

Remember, that Distribution = _____________, _______________, _______________

Which of the following is(are) easiest to compare with respect to distribution? Why?

|I. |II. |

|[pic] |[pic] |

|III. |IV. |

|[pic] |[pic] |

What is statistics all about?

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Number of Blue M & M’s in Bags of Plain M & M’s

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Distribution of Number of Blue M & M’s Based on My SINGLE SAMPLE!!!

|Sample |Number of Blue M & M’s |Total Number of M & M’s |Proportions of Blue M & M’s |

|Schaefer | | | |

|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|

0 3 6 9 12

Number of Blues

|----------|---------|---------|---------|---------|----------|---------|---------|---------|---------|

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Proportion of Blues out of ______

Class Results

|Student |Number of Blue M & M’s |Total Number of M & M’s |Proportions of Blue M & M’s |

|1 | | | |

|2 | | | |

|3 | | | |

|4 | | | |

|5 | | | |

|6 | | | |

|7 | | | |

|8 | | | |

|9 | | | |

|10 | | | |

|11 | | | |

|12 | | | |

|13 | | | |

|14 | | | |

|15 | | | |

|16 | | | |

|17 | | | |

|18 | | | |

|19 | | | |

|20 | | | |

|21 | | | |

|22 | | | |

|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|

0 3 6 9 12

Number of Blues

|----------|---------|---------|---------|---------|----------|---------|---------|---------|---------|

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Proportion of Blues out of ______

AND THE MORAL IS????

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Population

Class’s Samples

Parameter of Interest is

My Sample

Foundation (Theory behind) Statistical Inference

Probability, Random Variables, Families of RV’, and

Sampling Distributions

Statistical Inference

What does the sample statistic (eg [pic]) tells us about the population parameter (eg ()?

Corresponding Statistic

[pic]

M

S2

S

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Parameter of Interest

(popln

Medianpopln

(2popln

(popln

p

Population is:

Random

Sample

Method

Sample

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