INFO 1020 Week 4 Class Notes
INFO 1020 Week 4 Class Notes INFO 1020
Popular in Analytics II: Statistics and Analysis
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This 5 page Class Notes was uploaded by Alexandra Tilton on Sunday January 31, 2016. The Class Notes belongs to INFO 1020 at University of Denver taught by Ray Boersema in Winter 2016. Since its upload, it has received 24 views. For similar materials see Analytics II: Statistics and Analysis in Information System at University of Denver.
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Date Created: 01/31/16
INFO 1020: Analytics II Class Notes Mon. 1/25 Chapter 7a: Sampling and Sampling Distributions • Sampling Terminology • Population: Aset of ALL objects and corresponding data values for one variable - only ever one population • Sampling Frame: Asubset of the population which we use for the population when the population is not available • Example: Get the weights of 20 elephants •Population: is all elephants in the world •Sampling Frame: is all of those that are available to you (at the zoos) •Sample: is picking 20 elephants from those you ﬁnd at zoos • Sample: Extracted from the population, it is the set of SOME objects and their corresponding data values for one variable - thousands of samples • Calculate number of Possible Samples: =COMBIN(N,n) • Parameter: Some single number that describes the population (NOT USED FOR SAMPLES) •Example: size (N), mean (▯), standard deviation (σ), proportion that are of something (p) (i.e. over 10,000 feet) • Statistic: Some single number that describes the sample (NOT USED FOR POPULATION) Alexandra Tilton Page ▯1 of ▯5 • Example: size (n), mean (̄), standard deviation (s), proportion that are of something (p) (i.e. over 10,000 feet) • Finite Population: N is known and is static • Inﬁnite Population: N is not known and is dynamic • Point Estimate: Any known statistic of the sample size that is used as a best guess for an unknown parameter in the population • Simple Random Sample (SRS): If a population is ﬁnite we can do a trustworthy simple random sample • If this is done, all samples have an equal chance of being selected • 1: Number each population object • 2: =RANDBETWEEN(lowest, highest) • 3: Use this to pick n objects and their values • Random Sample (RS): If a population is inﬁnite we can do a trustworthy random sample • 1: =RANDBETWEEN(smallest count allowed, biggest count allowed) • Stratiﬁed Random Sample: Divide population into sections based on characteristics (i.e. majors) then pick randomly and proportionally from each group • Cluster Sample: Divide population into groups that have representatives of each kind of the characteristic (i.e. all have a ﬁnance major, an accounting major, a marketing major, etc.), then pick an entire group randomly • Systematic Sample: Population lined up and then pick every k item • Convenience: Picking whatever is convenient (i.e. your friends) • Judgement Sampling: Judging the population based on what you think will be informative Alexandra Tilton Page ▯2 of ▯5 INFO 1020: Analytics II Class Notes Mon. 1/27 Chapter 7b: Sampling and Sampling Distributions • Sampling Distribution A: The set of all x values and their associated probabilities • ̄ • B: The set of all p values and their associated probabilities • Find Sampling Distribution for x Valuē • Collect all x̄ • Use these to create a frequency distribution • Find Sampling Distribution for p Valueŝ • Collect all ps • Use these to create frequency distribution • What is the expected value of x? ̄ • The mean of all xs ̄▯ )x̄ • This will be equal to ▯ • What is the standard deviation of x? ̄ • STDEVxs (̄ ) x̄ • Thiσ will be less than σ • σx̄ / √n • As n increases, distribution gets tighter Alexandra Tilton Page ▯3 of ▯5 • If np ≥ 5, and if n(1-p), then the distribution of xs ī almost normal • If x distribution, then xs ̄re normal, regardless of sample size • The Central Limit Theorem (CLT) • ▯ x̄ • σ x̄σ/√n • The distribution of x is̄(almost) normal (see above) • Effect of Sample Size on Sample Distribution • As samples size, n, increases, the shape of the normal curve of x̄becomes narrower and higher • Practical Aspects of CLT • I know that my x is ̄lose to your x ̄ • I know that my x is ̄lose to ▯ • Calculate Probabilities • FOR SAMPLE AVERAGE: =NORM.DIST(x,▯ σ 1) x̄ x̄ • FOR ONE POINT IN POPULATION: =NORM.DIST(x,▯σ1) , , • What is the expected value of p ̂ • The mean of all p ̂ • Equal to original P (proportion) • What is the standard deviation value of p ̂ • The standard deviation of all p ̂ • √ p(1-p)/n • Calculate Probabilities • FOR SAMPLE PROPORTION: =NORM.DIST(x,p √ , p(1-p)/n,) Alexandra Tilton Page ▯4 of ▯5 Alexandra Tilton Page ▯5 of ▯5
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