# Chapter 9

**Created:**2011-01-26

**Last Modified:**2011-06-28

#### Related Textbooks:

Mind on Statistics (Available Titles Aplia)- number
- about some characteristic of a:
- population
- random circumstance
- population comparison

- population, not sample

- number
- summarizes characteristic of a sample

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

- use sample statistic to make conclusion about whole population parameter

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

- 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

- 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

- 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

- 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

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

- 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

- 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)

- 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

- 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)

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

- 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]

- 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

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

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