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Business Statistics 2


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The science that deals with the collection, classification, summarizing, organizing, analyzing and interpreting of numerical information
three areas of statistics
descriptive, statistical, prediction and regression
all of the items of interest in a given problem
finite subset drawn from the population
characteristic or property of interest
making a statement about a characteristic of the overall true population based on a characteristic from a random sample drawn from the population
statistical inference
can be described numerically; age, weight, height, size of family, monthly sales
quantitative data
categorical data; color of eyes, employment status, defect or no defect
qualitative data
difference between the estimator and the true population parameter; sampling info vs population info
sampling error
all other errors that cause a difference btw estimator and population parameter
nonsampling error
where every subset of fixed size in the population has equal probability of being included
random sample
a variable that contains the outcomes of a chance experiment
random variable
r.v. can take finite number of values (countable);think of as “separated values”
discrete random variable
r.v. can take any value in intervals (measurements);always infinite
continuous random variable
# of defectives in a lot of size 50, type of customer complaints
discrete random variable
wait time, response time of a computer system
continuous random variable
Each probability p(x) must be between 0 and 1 inclusive
probability distribution requirements
can only take on two values;
yes/no, pass/fail, etc.; n identical trials in the experiment; trials are independent
binomial random variables; characteristics of...
probability of success
probability of failure
relationship between p and q
p + q = 1
Relative frequency notion of probability
Binomial formula
Binomial table
Normal approximation to the binomial
4 methods for calculating binomial probabilities
It gives us the combination count, or the number of samples that produces exactly x successes in n trials
Binomial coefficient
4 things to describe descriptive statistics
location, dispersion, shape, data patters
measures of central tendency
mean, median, mode
measures of variability
standard deviation, variance, range, interquartile range
most frequently occurring observation in a distribution
middlemost observation in an ordered array
sum of all the values divided by the number of values (sample size or population size)
[max minus min]
measures of location that divide a group of data into four subgroups; lower quartile, middle quartile, upper quartile; Q(u)-Q(l); Range of the middle 50% of the distribution
Interquartile range
lower quartile
middle quartile
upper quartile
Tells how far on average each value is away from the mean; notation: population / sample
notation: population / sample
standard deviation
Standardized scores; Numerical value reflects the standing of a measurement relative to the mean; Tells how far away from the mean the value is in terms of standard deviations; Algebraic sign (+ or -) indicates whether the measurement is larger or smalle
data points that do not follow the general pattern of data
extreme values of the observed data
Based on the sample evidence; making a statement about the population
statistical inference
Based on known populations; making a statement about the probability of an event
act or process of observation that leads to a single outcome that cannot be predicted with certainty
the most basic outcome of an experiment
sample point
all of the sample points of an experiment
sample space
specific collection of sample points
probability rules for sample points
1) individual probabilities must lie between 0 and 1 (inclusive)
2) the sum of probabilities of all sample points in a sample space must equal 1
# of sample points that correspond to an event relative to the total # of sample points in the sample space
the event that A does not occur
complement of event A
if either A or B or both occurs
if both A and B simultaneously occur
if A and B have no sample space outcomes in common {AunionB contains no sample points}
mutually exclusive events
We have information – prior knowledge – that affects the probability of an event
conditional probability
if the occurrence of one does not alter the probability of the other
independent events
may take on any value in an interval
continuous rv
Make a statement about the overall true population parameters
Based on information from a random sample
statistical inference
Tells how far, on average the sample statistic is away from the population parameter; SE
st. dev. of sampling distribution
Mean of the sampling distribution of the statistic X-Bar equals the mean of the population; Standard deviation of the sampling distribution of the statistic X-Bar equals the standard deviation of the population divided by the square root of the sample si
central limit theorem
Provides a single value
Based on observations from 1 sample
Gives no information about how close the point estimator is to the unknown population parameter
point estimate
Provides a range of values
Based on observations from 1 sample
Gives information about closeness to unknown population parameter
Stated in terms of probability
To know exact closeness requires knowing population parameter that is usua
interval estimate
the measure of the precision of the estimate
margin for error
Involve qualitative variables
Fraction or % of population in a category
If two qualitative outcomes, binomial distribution
observed level of significance
probability of obtaining a test statistic more extreme (or than actual observed value given H0 is true

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