AP Statistics Midterm

x bar

Average of numbers in the sample which we use to guess what the real mean of the population is (μ)

SD

How spread out the data is (S or σ)

μ

True average or mean for the whole POPULATION, this is why when u define you have to say “true mean…”

p̂

The percentage of successes out of your SAMPLE SIZE

p

real population proportion (we want to find this but usually don’t have it so we use p hat)

p₀

Proportion stated in the NULL

z-score

a number telling us how far our result is from the expected value (null) if z increases, ex z=2, then the more unusual the result is

t-statistic

similar to z but used with means when the POPULATION SD is unknown so we use a sample SD

degrees of freedom

amount of information we have available, (n-1)

p value

The probability of getting a result this extreme if the null hypothesis is true, so a big p value means likely happen by chance because the results for extreme values given the null hypothesis is very likely too much for it to be an outlier.

alpha

cut off level for deciding if something is surprising or not.

ME

how far we might be from the actual answer

SE

estimated spread of the sampling distribution used to get ME

One sample z interval for a proportion

p hat ± z*(square root (p hat(1-p hat)/n))

One sample z TEST for a proportion

one sample z TEST is TESTING for the null switch the standard error formula from having phat to not z=p hat-p0/square root(p0(1-p0)/n)

One sample t-interval for a mean

x bar ± t*(s/square root(n))

One sample t TEST for a mean

t=xbar-μ0/(s/square root(n))

Two sample z interval for difference in proportions

(phat1-phat2) ± z*(SE for phat1-phat2)

Two sample z TEST for difference in proportions

USE formula with Pc: z=phat1-phat2/(use formula when p1-p2, sphat1-phat2=…)

Pc formula

X1+X2/(n1+n2)

Two Sample t-interval for difference in means

(xbar1-xbar2) ± t*(on formula sheet S of differences in X bar)

Two sample t test for difference in means

t= (xbar1-xbar2)/(formula for standard error of diff in x-bars

test stat=stat-para/standard error translates to…

observed-expected/spread

test uses…

z/t formula

interval uses…

estimate ± standard error