MATH1342
S08 – 7:00A-8:15A T/R
BB218
SPRING 2014
Daryl Rupp
What proportion of southern Iowa homes
have soft water? A sample of 6 homes in 6
cities found 3 had soft water. What is the
conclusion?
1. 0.50 of the homes in southern Iowa have soft
water.
 2. Approximately 0.50 of the homes in southern
Iowa have soft water.
 3. We can not make a conclusion.
 4. Between 0.33 an 0.67 of the homes have soft
water,
 5. There is an 80% confidence that between 0.33
and 0.67 of the homes have soft water.
NOTE: See Problem 10 of the homework for a great
example
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STATISTICS
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The science of collecting, organizing,
summarizing and analyzing data to draw
conclusions or answering questions, with a
given amount of confidence concerning
the answer.
In other words, it is the method or
process used in finding an answer to a
question, with a specific amount of
confidence that the answer is correct.
THE SCIENTIFIC METHOD
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1. Define the question & scope to be investigated
2. Gather information & resources to define
hypothesis
3. Perform experiment & gather data
4. Analyze date
5. Interpret data and draw conclusion which may
lead to a starting point for continued investigation
6. Retest to verify results (usually done by others)
or revise hypothesis and start new investigation
TWO TYPES OF STATSISTICS
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Descriptive is about organizing and
summarizing data in order to picture the
nature of the population or sample
represented by the data. (Ch’s 2 – 3)
Inferential is the process or method of
generalizing the results from a sample to
the entire population and measuring the
reliability of that answer (Ch’s 9 – 11, 4)
DEFINITIONS
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POPULATION: The entire group of
individuals being investigated (size is N).
Must be precisely defined.
INDIVIDUAL: One member of the entire
group or population.
SAMPLE: A subset of individuals of a given
size (n) taken from the population.
DEFINITIONS
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VARIABLE: A given aspect of an individual. This
would be the definition of the aspect. For example, if
a population or sample consists of people then the
variable could be weight, height, color of eyes,
gender, etc. What aspects could be found for a
individual country?
DATA: The possible observations or outcomes for a
variable concerning individuals. This is a label or a
count of a measurement.
CHARCTERISTIC: A summary of a numerical variable
of a population or sample such as mean, max, range
or standard deviation. Label data can not be
summarized.
DEFINITIONS
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DATA CONSISTS OF ATTRIBUTES (Labels):
Colors, Judgments, Grades (as is A, B, C, D,
F), Names.
DATA CONSISTS OF NUMBERS FROM
MEASUREMENTS OR COUNTS: Weights,
Polls, Surveys, Temperatures, Lengths,
Bowling scores, Number of Home Runs.
DEFINITIONS
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Characteristics (numerical) that come from
the POPULATION are called PARAMETERS.
Characteristics (numerical) that come from
a SAMPLE are called STATISTICS.
If the data comes from labels then not
called either (as no numerical summary is
possible for Qualitative data).
DEFINITIONS
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QUALITATIVE DATA comes from LABELS.
QUANTITATIVE DATA comes from
NUMERICAL data
DEFINITIONS
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DISCRETE DATA comes from counts and
are whole numbers (have no decimal
parts).
CONTINUOUS DATA comes from
measurements and are real numbers (may
have decimal parts)
NOTE: LABELS are neither
A SIDE NOTE
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Statistics is all about the number line.
Draw a number line for the interval 0 to 5.

Draw a number line centered at o and going 6
units in each direction.
Draw a number line for the interval – 3 to +3.
Draw a number line from – infinity to infinity
DEFINITIONS
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TWO METHODS OF OBTAINING DATA:
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OBSERVATION: Data from observing, only.
Not interfering with the process in any way.
EXPERIMENTATION: Data from controlling
some factors of a process. Often involves
comparing results of two or more values of a
control factor. Involves the interference by
the investigator.
LEVELS OF
MEASUREMENT
(Defines how data can be analyzed)
Nominal: Values of the variables are names or
labels; they can not be ranked or ordered (like
color of eyes).
Ordinal: Values of the variables are names or labels
but they can be ordered but no numeric value so
cannot find differences (like letter grades)
LEVELS OF MEASUREMENT
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Interval: Values of the variables have the
property of being ordered and can be
compared (find real differences) but have
no absolute zero (like temperature).
Ratio: Values of the variables are like
interval, but have absolute meaning –
there is a 0 values that means that
absence of value (like weight)
SPECIAL NOTE
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The data you collect is not the answer or
analysis to the question you are
investigating.
The data you collect is the result of the
question you ask or the instructions you
give.
Examples
TYPES OF SAMPLING
Sampling: Obtaining the data from a
number (size n) of individuals from a
population (size N).
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Simple Random Sampling: Where every
individual in the population has an equal
chance of being selected. The best and
the goal of sampling methods.
TYPES OF SAMPLING
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Stratified Sampling: Separating the
population into non overlapping groups
(strata) and then selecting simple random
samples from each group.
Systematic Sampling: Obtained by
selecting every kth member of the
population.
TYPES OF SAMPLING
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Cluster Sampling: Dividing the population
into groups (or clusters) and selecting all
the individuals from that cluster.
Convenience Sampling: Individuals are
selected on the ease of obtaining them
and not randomly from the population.
Voluntary Sampling (Type of
convenience): Worst possible.
See section 1.4 for complete discussion of
sampling methods
BIAS IN SAMPLING
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Always Try to Avoid Bias
Two Types: Intentional and Unintentional
Sampling: Method tends to favor one
section of population. One section is
under represented.
Non-response Bias: From Voluntary
Sampling where individuals can refuse to
take part.
BIAS IN SAMPLING
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Response Bias: Answers do not reflect
true feelings of responder Caused by:
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Interviewer error, the way the question is
framed;
The choices and wording offered in survey;
Order of questions or responses
Plain old entry error.
See 1.5 for complete discussion
Easy to Deceive
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Can be done graphically.
Can be done numerically by focusing on
numbers rather than relative proportion.
Can be done by fudging numbers.
EXPERIMETAL TYPES
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CONTROL FACTORS: All processes have
random results, but the results can be
somewhat limited through control factors. By
changing these factors the results can be
changed.
BLIND STUDIES: Can lead to Bias.
DOUBLE BLIND STUDIES: The best. Used in
many medical studies. Can involve the use
of placebos or another medication.
EXPERIMETAL TYPES