stats exam 3

descriptive stats

taking population data, taking a sample size of n/a cenus → using that to create graphs, table, summaries

focusing on central tendency (mean, median, mode), variability (range, standard deviation, variance), and distribution shape

inferential stats

taking a sample size of n from a population → calc the sample stats → make an inference about a population parameter

characteristics of a good sample

representative of the population and is independent (large sample and random sample)

simple random sample (SRS)

every element in the population is equally likely to be in the sample

how? first, get asampling frame , then choose at random from the list

stratified random sample, why is created and how is it created?

means “layered”

why: to avoid underrepresentation

how: separate population into strata (groups) based of classification criteria ,then sample separately from each stratum proportional to the stratum size

stratified random sample RESULT

higher prescision, no underrepresentation, higher expense

clustered random sample, why? and how?

clustered = groups

why? there is more variability within a cluster than between the clusters

how? randomly select one or more clusters and sample all elements from each

clustered random sample result

less expensive and less precision

what is sample stats used to estimate? where is the sample stat found from?

used to estimate a population parameter that is fixed but unknown

where is the sample stat found from: observed data

list of sample stats

x bar, s, p bar

list of population parameter

mew, signma, p

what are estimators

RANDOM VARIABLES

estimates vs point estimates vs estimators

estimates and point estimates: actual value

estimators: x bar, p bar, s, r, s²

error

any difference between the estimator and the parameter

estimator vs parameter

Estimator: a sample statistic that reflects an average/summary metric for a given population parameter.

Parameter: A particular attribute of a population.

sampling error

error due to taking a sample

the UNAVOIDABLE difference between sample and population controllable =and quantifiable

non-sampling eorror

any other kind of error - leads to BIAS

bias

a systematic difference between the sample and the population

selection bias

sample differs systematically from the population due to sample selection (eg convenicne sampling)

nonresponse bias

not enough response (polling)

response bias

responses are bad (polling)

sample dist

the probability dist for an estimator (a sample stat)

sample mean

x bar

how is the sample mean (x bar) distributed?

normally

what is the mean and Variance for x bar

E(x bar) = mew

var(x bar) = sigma²/n

two formulas for Z-score

ignore the blue:

when doing binomial problems for Z-score, what is the p-value in the equation

the p-value the is probability of ANY randomly selected thing gets what the problem is asking. this means to not use the p value you get from a specific sample size/the sample size that x equals in the binomial. so for this example, use the answer you got from a) for part c)

central limit theorem for sample mean (x bar)

x1…xn are a random sample of size a from any population with mean mew and standard deviation sigma, then x bar is approx normally dist if n is greater than 30

how to find sigma

sqrt of var(x)

to find variance, what range do you use in the nuemerator?

the GIVEN range, not the range of the x values you’re trying to find

when do you know to use CLT for sample mean

if you’re trying to find the probability of the sample mean (x-bar) being a certain value, and n is greater than 30

Summary: Sampling distribution of x bar. If X1-Xn are a random smaple from ANY population with mean mew and variance sigma squared, then…

sample proportion

p hat/bar

outcome over interest/total outcomes

what is the sample proportion p bar used for

to estimate p, the POPULATION proportion

what do these mean

CLT for the sample proportion

the sample proportion is approx normal dist if n is large enough relative to p

CLT for the sample proportion - two things you must check

are there separate z formulas for sample mean and sample proportion

yes! on the formula sheet. you use those when you need to find probability of either a sample mean/proportion being a certain value

what does standard error equal

standard dev = sqrt of var

CLT for the sample proportion - what do you do after you check the two required things

apply the z-score stuff to find probabilities! same old same old. just make sure to use the z-score formula for p hat on the formula sheet

confidence interval estimate

a range of values that contains the population parameter with a specified level of confidence

format for confidence interval

what info does margin of error contain

sample size, population variability, confidence level

what is a 95% confidence interval associated with for its z-score

z=1.96 (plus or minus)

what does alpha show for confidence intervals

the probability of a confidence interval NOT includinhg the population parameter.

what does (1-alpha) show

probability that the interval WILL include a population parameter

what is this

is the value of a standard normal variable with upper-tail probability alpha/2

notation for upper tail probability (?)

and if you multiple that by 2 you get the width

for upper-tail probability, what happens when sigma goes up? how about n? how about confidence level?

sigma up, width up

n up, width down

conf level up, width up