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Notes: Chapters 4 and 5

by: Amanda Furtick

Notes: Chapters 4 and 5 ESC_PS 4170 - 06

Amanda Furtick
GPA 3.8

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These notes cover the main ideas of chapters 4 and 5.
Intro to applied statistics
Class Notes
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This 4 page Class Notes was uploaded by Amanda Furtick on Tuesday September 13, 2016. The Class Notes belongs to ESC_PS 4170 - 06 at University of Missouri - Columbia taught by Beiner in Fall 2016. Since its upload, it has received 7 views. For similar materials see Intro to applied statistics in Math at University of Missouri - Columbia.

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Date Created: 09/13/16
Introduction to Applied Statistics   Chapter 4  Objectives:  I. Discuss the language of mathematics  A. ‘A’ and ‘B’ and ‘X’ and ‘Y’ are used to represent a quantity, score, or value  within a variable. ‘N’ is used to represent a number of something.    II. Distinguish between the independent variable and dependent variable  A. An independent variable is the main variable that is used to determine if it has an  effect on another variable (the dependent variable). The dependent variable can  only be determined by the independent variable and relies on that for its outcome.  (ie: “Is number of pounds overweight related to systolic blood pressure?” The  number of pounds overweight would be the independent variable and blood  pressure would be the dependent variable because the blood pressure is depending  on how much overweight a person may be.)  III. Distinguish between descriptive and inferential statistics  A. Descriptive statistics classifies numerical data (ie: how many students are in the  classroom? How many are male? How many are female?) Inferential statistics  makes a guess about the population based on a smaller portion of the population  (a sample.)   IV. Describe the types of data that can be collected  A. Nominal data is a name or category. It is simply an identification number, not a  number of value. (ie: A football player’s jersey number simply identifies him, not  ranks his position). Ordinal data is the order or category of numbers. (ie: when  people are lined up by height, you would order them in 1st, 2nd, 3rd from tallest  to shortest). However the differences between the rankings are NOT the same (the  1st person could be 4 inches taller than the 2nd, but the 2nd could only be 1 inch  taller than the 3rd). Interval data is the opposite or ordinal data. The space  between each number is equal (The difference between one degree to the next of  temperature is just one degree. Always.) Also, zero does not reflect the absence of  something. (Zero degrees does not mean the absence of temperature, it is an  actual temp). Ratio measures the same as an interval (equal distance between two  numbers) but DOES represent the absence of zero (zero pounds means there is no  weight).     Definitions:  ­ Datum ­­ singular of data  ­ Parameter ­­ description of a population   ­ Statistic ­­ a number which summarizes data collected on any part of a population  (sample)  ­ Population ­­ complete set of measurements of any characteristic  ­ Sample ­­ subset of the population   ­ Parametric statistics ­­ conducted on data sets upon which certain assumptions are made.  (interval, ration, homogenous)   ­ Nonparametric statistics ­­ conducted on data sets which do not meet parametric  assumptions (nominal, ordinal, not homogenous)    Chapter 5  Objectives:  I. Define probability  A. Probability is the likelihood or chance that something is the case of will happen. It  provides a numerical measure of the likely occurance of a particular event. 0 = an  event will never occur.  .5 = event and “not event” are likely. 1 = the event will  always occur  II. Describe probability rules  A. All probabilities between 0 and 1 are inclusive. 0 <= P(E) <= 1  B. The sum of all the probabilities in the sample space is 1.   C. The probability of an event which cannot occur is 0.  D. The probability of an event which must occur is 1.’  E. The probability of an event not occurring is one music the probability of it  occurring. [1 ­ P(E)]  III. Distinguish discrete probability distribution and continuous probability distribution.  A. Discrete Probability Distribution ­­ describes a finite set of possible occurrences   B. Continuous Probability Distribution ­­ describes an unbroken continuum of  possible occurrences     Definitions:  ­ Experiment ­­ a situation involving chance or probability that leads to results called  outcomes  ­ Outcome ­­ the result of a single trial of an experiment   ­ Sample Space ­­ the set of all possible outcomes (ie: sample space of rolling a die is 1, 2,  3, 4, 5, 6)  ­ Event ­­ one or more outcomes of an experiment (ie: rolling a 3 is an event)  ­ Probability ­­ the measure of how likely an event is (ie: the probability of rolling a 3 is  one sixth)   ­ P(E) = number of outcomes corresponding to event E/total number of outcomes   ­ 1 ­ P(E) = probability of something NOT occurring   ­ Subjective Probability ­­ an individual’s personal judgment about how likely a particular  event is to occur  ­ Random Variable ­­ a function that associates a unique numerical value with every  outcome of an experiment   ­ The probability of any exact value is equal to 0.  


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