Business Statistics 2
Terms
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- The science that deals with the collection, classification, summarizing, organizing, analyzing and interpreting of numerical information
- statistics
- three areas of statistics
- descriptive, statistical, prediction and regression
- all of the items of interest in a given problem
- population
- finite subset drawn from the population
- sample
- characteristic or property of interest
- variable
- 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 valuesâ€
- 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
- p
- probability of failure
- q
- 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
- shape
- skew
- most frequently occurring observation in a distribution
- mode
- middlemost observation in an ordered array
- median
- sum of all the values divided by the number of values (sample size or population size)
- mean
- [max minus min]
- range
- 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
- 25%
- lower quartile
- 50%
- middle quartile
- 75%
- upper quartile
- Tells how far on average each value is away from the mean; notation: population / sample
- variance
- 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
- z-score
- data points that do not follow the general pattern of data
- outliers
- extreme values of the observed data
- whiskers
- 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
- probability
- act or process of observation that leads to a single outcome that cannot be predicted with certainty
- experiment
- the most basic outcome of an experiment
- sample point
- all of the sample points of an experiment
- sample space
- specific collection of sample points
- event
- 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
- probability
- the event that A does not occur
- complement of event A
- if either A or B or both occurs
- union
- if both A and B simultaneously occur
- intersection
- 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 - Proportion
- observed level of significance
- p-value
- probability of obtaining a test statistic more extreme (ï‚£ï€ or ï‚³ï€©ï€ than actual observed value given H0 is true
- p-value