Ch 3

measures of center: mean for a sample is denoted-

x̅

measures of center: mean for a population is denoted-

μ

correlation for a population is denoted with ________.

ρ

standard deviation for a population is denoted :

σ

if we were finding a 96% confedence interval, 1. keep the middle 96%. How much is left for the ends? __________ 2. The lower bound would be the _______ percentile 3. the upper bound would be on the ___________ percentile 4. if our bootstrap distibution contained 1000 boot strap statistics, how many values would we chop off of each end?

1. 4% total (2% on each end) 2. 2nd 3. 98th 4. 2% of 1000 = (.02)(1000) = 20 pts off each side

Cautions: 1. for 95% Confidence intervals, the ________ method or _______may be used. For other Confidence levels, we will use the percentile method (for now). 2. these methods only work in the distribution is reasonably ________ and __________. if it is highly skewed or looks "spiky" with gaps we cannot find a confidence interval using our methods.

1. standard error; percentile method 2. symmetric and bell shaped

which is wider, 90% confidence interval or a 95% confidence interval?

95%

Notation for the statistics we have been learning:

P (hat), x (bar),s, r,etc

A ________ is a number that describes some aspect if the _____.

Parameter; Population

A ______ is a number that is computed from data in a ____.

Statistic; sample

a __________ is a random sample taken with replacement from the original sample. it must be the same size as the original sample.

boot strap

a ______________ is the distribution of many bootstrap statistics. It is centered around the _______ in the same way that sampling distributions are centered around the population parameter.

boot strap distribution; sample statistics

a _____________ is the statistic computed on a sample sample.

boot strap statistic

what if we can only get one sample (to make a sampling distribution we need many samples!) what if we want confidence intervals with confidence levels other than 95%? this is where ____________ come in handy.

bootstrap distributions

the more ____________ you use, the more ___________ your confidence interval will be. for the purpose of this class, 1000 samples are sufficient. In real life, you would probably want to use 10,000 or more bootstrap samples.

bootstraps samples, accurate

now, more specifically, we will look at what we call _________ ______________: these are interval estimates computed from sample data by a method that will capture the _________ for a specified proportion of all samples. the success rate is the _____________.

confidence intervals; parameter; confidence levels

our __________ tell us how many samples give intervals that contain the true parameter, so we can say we are that confident that one interval contains the true parameter.

confidence level

since statistics vary from sample to sample, a point estimate is often insufficient. in these sections, we will instead find a range of possible values for the population parameter called an ____________________.

interval estimate

for most of the statistics we consider, if the sample size is ______________ the sampling distribution will be ______ and _______.

large enough; symmetric; bell shaped

if we took the samples of size 1000 instead of 500, and used the sample proportions to estimate the population proportion: would the estimates be more accurate or less accurate? would the standard error be larger or smaller?

more accurate smaller

imagine the ________ is many, many copies of the original sample. we must assume that the sample is _________ to simulate a sampling distribution, we sample ______ from the sample that we have. (we could select the same case more than once).

population; representative of the population; with replacement

proportion for a sample is denoted with _____

p̂

Correlation for a sample is denoted with ______.

r

standard deviation for a sample is denoted:

s

In the last section, we looked at sample statistics and population parameters along with their notation. we used the ____________ to estimate the corresponding ___________. this is called a ____________.

sample statistics; population parameter; point estimate

A ________________ is the distribution of sample statistics computed for different samples of the _________ from the same population.

sampling distribution; same size

the __________ of statistic is the standard deviation of the sample statistic. As the sample size __________, the variability tends to ___________ and the sample statistics will be closer to the _____________.

standard error; increases; decrease; population parameter

95% confidence interval is approximately:

statistic (+ or -) 2 times standard error

Interval estimate:

statistic (+ or -) margin of error

proportion for a population is denoted with _____

p

remember: the _________ (what is true about eh population) is a fixed value; it does not change. It is a sample that is prone to ________.

parameter; vary

if the bootstrap distribution is symmetric and bell-shaped a 95% CI can be estimated by _____________, where SE is estimated by the standard deviation of the bootstrap distribution.

statistic (+ or -) 2SE

if we have a ________, ____ distribution, _____% of our data falls within 2 standard deviations. So, we can assume the sample statistic falls within 2 standard errors of the parameter about ___% of the time. (we will use this to approximate a 95% confidence interval).

symmetric, bell shaped, 95%, 95%

If the boot strap distribution is approximately ____, we can construct a confidence interval by finding the ______ in the bootstrap distribution so that the proportion of bootstrap statistics _____ the percentiles matches the desired confidence level.

symmetric, percentiles, between