Chapter 9

Statistics 250 with Gunderson at University of Michigan - Ann Arbor

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By: Jen W.
Textbook:

Mind on Statistics (Available Titles Aplia)
Created: 2011-01-26
Size: 19 flashcards
Views: 102

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parameter

number
about some characteristic of a:

population
random circumstance
population comparison

**different from population of interest: whole group vs. (here) whole group's characteristic we want to study

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)

**possible values of the statistic when we take random samples from 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

By: Jen W.
Textbook:

Mind on Statistics (Available Titles Aplia)
Created: 2011-01-26
Size: 19 flashcards
Views: 102

About StudyBlue

“I have been getting MUCH better grades on all my tests for school. Flash cards, notes, and quizzes are great on here. Thanks!”
Kathy