Analyzing Proportions Flashcards
what is a proportion
the fraction of a population bearing some trait
how does proportion apply to statistic s
its the probability that an individual chosen from a population will bear the trait of interest
what numbers are proportions between
0 and 1
what does the binomial distribution apply towards
measurements that can be divided into two mutually exclusive groups
what is the general outcome for a binomial distribution/test
success (shows the desired outcome) or failure (does not show the desired outcome)
what is the binomial distribution
the probability distribution for the number of successes in a fixed number of trials when the probability of each success is THE SAME FOR EACH TRIAL
what variable represents number of successes
X
what variable represents the number of independent trials
n
what variable represents the probability of success for each trial
p-hat
what are important assumptions for n in a binomial distribution
- separate trials are independent
- probability of success (p) is the same in every trial
describe the binomial distribution equation
how to calculate “n chose X”
when do we have an unbiased estimate
when the mean sampling proportion= population proportion
how does a graph show a more precise sampling proportion value
the narrower spread of the data = more precise p-hat value
what is the binomial test
a test that uses data to test whether a population proportion (p) matches a null hypothesis expectation for the proportion
what is a null hypothesis for binomial test
relative frequency of successes in the population is the expected null hypothesis proportion (po)
what is an alternative hypothesis for binomial test
the relative frequency of successes in the population is NOT the expected null hypothesis value
is the alternative hypothesis in a binomial test two sided or one
two sided
( can either be above or below the null hypothesis expectation)
when do we reject a null hypothesis in binomial testing
if the P-value calculated in below the significance level
how do you calculate p-hat (the sample proportion)
what is the binomial test OVERVIEW
whether a population proportion (p) matches a null expectation (po)
what does a binomial test assume
random sample
what is the test statistic in a binomial test
observed number of successes (X)
when is an approximation of P values done
when n and X and huge numbers
does a binomial test give an exact or approximate P value
EXACT P value
what are the goals of estimating proportions
- estimate the population proportion (phat)
- estimate the standard error of proportion (SE p-hat)
- estimate confidence intervals for proportions
what is standard error
the standard deviation of the sampling distribution
how to calculate standard error of the proportion
how to calculate confidence intervals with Wald Method
where Z is 1.96
how to calculate confidence intervals with Agresti-Coull Method
