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**information on: sample statistics, not individual values

parameter

- number
- about some characteristic of a:
- population
- random circumstance
- population comparison

population parameter

- population, not sample

statistic (sample statistic)

- number
- summarizes characteristic of a sample

sample estimate

- estimates value of population parameter that we don't know

statistical inference

- use sample statistic to make conclusion about whole population parameter

confidence interval

- interval
- covers range the true value of population parameter lies in that:
- we currently don't know
- estimates what true value is

hypothesis testing (significance testing)

- uses sample data
- reject hypothesis about population
- pick null value for parameter: means nothing happens
- i.e. weight-loss clinic thinks average weight loss for customers is 0
- method: get sample, find sample statistic, figure out:
- if null parameter value is right
- then: how unlikely would sample statistic occur?
- statistical significance:
- if null parameter value is right, then observed values can't be right also

the big 5 parameters

- proportion in a category
- difference between two populations' proportion in a category
- mean of quantitative variable
- mean of paired differences for quantitative variable
- difference between two populations' mean of quantitative variable

proportion falling into a category

- population parameter: p = proportion in population that falls into that category
- sample estimate: p^ = proportion in sample falling into that category
- ex: 46% volunteers in random experiment are assigned to wear nicotine patch. Sample is 120 volunteers.
- population: all smokers
- parameter: probability (in %) that randomly selected person from population would quit smoking after wearing patch.
- sample statistic: proportion in sample who wear patch will quit smoking

difference between two populations' proportion in a category

- population parameter: p1 - p2 = difference in two population proportions
- sample estimate: p^1 - p^2 = difference in two sample proportions
- useful for comparing 2+ populations
- ex: nicotine patch wearers vs. placebo quitting smoking (46% vs. 20%)
- p1 = prob. placebo patch will quit
- p2 = prob. nicotine patch will quit
- parameter: p1 - p2 = diff in pop proportions of quitters if wearing placebo instead of nicotine patch
- sample statistic: pbar1 - pbar 2 = diff btwn proportion of sample of quitters

mean of quantitative variable

- population parameter: u = population mean for variable
- sample estimate: x bar = sample mean for variable
- average of variable of interest for all in population

mean of paired differences for quantitative variable

- population parameter: Ud = population mean of differences in two measurements
- sample estimate: d bar = mean of differences for sample of two measurements
- paired diff: diff. in matched pairs
- ex: college students diff. btwn left vs. right handspan, took sample (average = 0.16)
- parameter: Ud = population mean diff in left vs right span for college student pop
- sample statistic: d bar = 0.16

difference between two populations' mean of quantitative variable

- population parameter: u1 - u2 = mean differences between two populations
- sample estimate: xbar1 - xbar 2 = mean differences between two sample means
- independent samples (not related at all)
- ex: average age of first intercourse for male vs. female teens
- u1, u2 = age at first intercourse for population of teen males and teen females
- parameter: u1 - u2 = pop. mean ages at first...difference
- sample statistic: xbar1 - xbar 2 = -0.7 (numbers given)

sampling distribution

- distribution of:
- probabilities
- of all possible values
- of a statistic
- for repeated samples of same size (from same population)

**information on: sample statistics, not individual values

general format for sampling distributions

- approximately normal
- mean = population parameter (of a sample statistic)
- standard deviation = how much sample statistic's values across different samples (from same population)
- sampling distribution for sample mean = standard deviation of xbar
- for sample proportion = standard deviation of p^
- larger sample sizes = less variability (more stable)

standard error

- estimate of:
- standard deviation for sampling distribution
- one for Xbar (std of xbar)
- one for p^ (std of p^)

normal curve approximation (sampling distribution of p^) rule for sample proportions

- let:
- p = proportion of interest in population or binomial prob of successes
- p^ = proportion/(of successes) in sample
- then to be a normal curve distribution:
- mean = p (probability)
- std = s.d(p^) = sq.rt of [p(1-p]/[n]

normal curve approximation conditions

- must have actual, physical population (or repeated trials) with: fixed proportion (or fixed relative frequency probability)
- select random sample from population or outcomes for each trial is independent
- large sample or trials: np and n(1-p) should be at least 10

standard error of p^

- s.e(p^) = sq. root of [p^(1-p^)]/[n]
- estimates std of sampling distribution for sample proportions
- only based on ONE SINGLE SAMPLE

About this deck

Author: Jen W.

Textbook: Mind on Statistics (Available Titles Aplia)

Created: 2011-01-26

Updated: 2011-06-28

Size: 19 flashcards

Keywords: flash card flashcards digital flashcards note sharing notes textbook wiki college dorm class classroom exam homework test quiz university college education learn student teachers tutors share, study blue studyblue studyblu

Views: 120

Textbook: Mind on Statistics (Available Titles Aplia)

Created: 2011-01-26

Updated: 2011-06-28

Size: 19 flashcards

Keywords: flash card flashcards digital flashcards note sharing notes textbook wiki college dorm class classroom exam homework test quiz university college education learn student teachers tutors share, study blue studyblue studyblu

Views: 120

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